A cosmological model described by the perturbation metric is proposed, in which space is entrained by matter expanding as a result of the Big Bang. In the absence of an input of external energy and momentum, the solution of the Einstein equations assumes a pressure equal to zero and an accelerated expansion. The cosmological perturbation model explains the difference in measurements of the Hubble constant using gravitational lensing and a distance ladder.

This article introduces a new MfEIT UDESC Mark I system, which consists of a 32-electrode setup featuring a modified Howland current source, low cost, portable and non radiation. The system is capable of reconstruction of electrical conductivity tomographic images at a rate of 30.624 frames per second and about 5 minutes for imaging. The current source employs 0.5 mA, adjacent current application pattern with frequencies ranging from 10 kHz to 1 MHz. The article outlines the hardware, firmware, and software design specifications, which include the design of the current source, calibration procedures, and image reconstruction process. Tomographic images of conductivity were reconstructed in ex vivo healthy pig lungs and those with pneumonia, as a proof of concept for future applications in live pigs. The high spectral power density, combined with real-time system calibration provides clinical advantages in veterinary medicine. The goal is to identify lung areas affected by Mycoplasma hyopneumoniae in pigs, through the analysis of electrical conductivity difference, offering a valuable tool to assist veterinarians for to obtain images of respiratory diseases. The reconstruction method (GREIT) was evaluated with experimental data and It was compared with the Gauss-Newton and Total Variation methods, where GREIT proved to be superior.

In general, a superconductor has zero resistance, although it requires significant refrigeration or high pressures with high manufacturing costs, which prevents it into practical applications. In other words, solving these issues implies main superconducting researches. To solve these problems, this paper describes a new type of superconductivity, which is independent for temperatures and which operates without pressures. The principles of the presented system are as follows:First a voltage source, a current source and a load are connected in series. Then, the voltage of the voltage source is adjusted to balance the voltage of the load. Under this condition, the balance of the two voltages provides a zero voltage between the taps of the current source and the generated current from the voltage source becomes zero because of the internal infinite resistance of the current source. As a result, the electric powers generated by the two sources are zero, and therefore, the load cannot generate Joule heating because of energy conservation. However, the current from the current source (not the voltage source) is not zero; therefore, we can predict that the resistance of the load must be zero. As a theory, we derived a new electric field and transient attractive force, which result in a very short coherence of an electron pair because there is not the Coulomb repulsive force due to the existence of the above transient attractive force. Note that both the forces are derived by the Poisson equation, which implies that they cannot be compatible. Therefore, the pair combination energy from spins becomes extremely strong, which is not destroyed by the normal heat energy. Moreover, every center-of-mass motion of electron pair results in the Bose-Einstein condensation and the macroscopic wave function, which produces the London equation (i.e., the Meissner effect). Moreover, by introducing the equivalent circuit, this paper conducted numerical calculations. As a result, we could derive numerically zero resistance and responses for additional static magnetic fields as a discharged current, which implies the Meissner effect. Note that this paper has prepared Appendix section, which provides a guide to reproduce actual experiments and preliminary experimental results. These results in the Appendix indicate the zero resistances and Meissner effects.

The existence of semantic inaccuracy §2 articles by A. Einstein “On the electrodynamics of moving bodies”, illustrating the principle of the relativity of simultaneity. In a sentence “The observers co-moving with the moving rod would thus find that the two clocks do not run synchronously while the observers in the system at rest would declare them synchronous”, the preposition “not” must be moved and placed before the word “synchronous”, at the end of the sentence. The criterion for synchronism of the clocks on the rod is the time it takes for the beam to travel from clock A to clock B and back, and for observers on the rod it will be the same both when the rod is at rest and when the rod is moving. Otherwise, observers on the rod would have had at their disposal an experiment that would allow them to determine whether the rod is moving or at rest, which contradicts the first postulate of the Special Theory of Relativity. The inaccuracy is found unchanged in modern editions in English and Russian, and can become a source of difficulties when teaching the basics of the Special Theory of Relativity based on primary sources, as well as make it difficult to understand the author’s logic when studying independently. Nobel laureate R. Feynman, having expanded and modified A. Einstein's thought experiment, eliminated the inaccuracy described in the article.

Information geometry (IG) seeks to characterize the structure of statistical geodesic models from a differential geometric point of view. By considering families of probability distributions as manifolds with coordinate charts determined by the parameters of each individual model, the tools of differential geometry, such as divergences and metric tensors, provide effective means of studying their characteristics. The research undertaken in this paper presents a novel approach to the modelling study of information geometrics of a queueing system. In this context, the manifold of a stable M/G/1queue is characterised from the viewpoint of IG. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of stable M/G/1 queue manifold are devised. In addition to that, new results that uncovered the significant impact of stability of M/G/1 queue manifold on the existence of (IFIM) are obtained. The Kullback’s divergence (KD), and J-divergence (JD).New result has been devised on the significant impact of both server utilization and squared coefficient of variation of the underlying M/G/1 queue manifold on both (KD) and (KD) are devised. Also, it is revealed that stable M/G/1 QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of M/G/1 queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability and the instability phases of the underlying M/G/1 queue manifold. Furthermore, a new discovery that presents the significant impact of stability of M/G/1 queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. It is also shown that the obtained (IME) is unstable. Also, it is shown that stability of the devised (IME) enforces the instability of M/G/1 queue manifold. Unifying IG with Queueing Theory enables the study of dynamics of queueing system from a novel Riemannian Geometric (RG) point of view, leading to the analysis of the stable M/G/1 queue, based on the Theory of Relativity (TR).Extending the study over two new additional divergence measures, namely and together with a complete illustrative numerical results for all these measures including KD, JD. This links Queueing theory, IG with deep machine learning and metric learning. Furthermore, this reveals the revolutionary approach of queue learning. Full analytic study of Gaussian curvatures subject to both Angular and Monge techniques together with the overall stability dynamics impact on these curvatures. Full analytic study of Einestein Tensor and Stress Energy Tensor together with the overall stability dynamics impact on these curvatures. The inclusion of the definitions of Gaussian and Ricci, Ricci scalar curvatures and Einstein Tensor together with their physical interpretations; The proposed novel approach for the pioneer visualization of queueing systems via computational information geometry. The determination of new important links between classical queueing theory and other mathematical disciplines, such as IG, matrix theory Riemannian geometry and the THEORY OF RELATIVITY by providing for first time i) The full detailed derivations of the Gaussian curvature ii) The Ricci curvature tensor and iii) The full physical as well as the geometric interpretation of these new results. The provision of a novel link between Ricci Curvature (RCT) and the stability analysis of the stable M/G/1 QM. The full investigation of the newly introduced QT-IG unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them. The full investigation of the newly introduced (QIGU) unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them.

From a differential geometric perspective, information geometry (IG) aims to characterise the structure of statistical geodesic models. The research done for this paper offers a novel method for modelling the information geometry of a queuing system. From the perspective of IG, the manifold of the transient M/M/infinity queue is described in this context. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of transient M/M/infinity QM are devised. In addition to that, new results that uncovered the significant impact of stability of QM on the existence of (IFIM) are obtained. Moreover, the Geodesic equations of motion of the coordinates of the underlying transient are obtained. Also, it is revealed that stable QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of transient M/M/iInfinity queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability(instability) phases of M/M/Infinity QM. Furthermore, a new discovery that presents the significant impact of stability of queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. Also, it is shown that stability of the devised (IME) enforces the instability of M/M/ Infinity QM. More interestingly, novel relativistic info-geometric queueing theoretic links are revealed .

If we assume that: a. The four fundamental forces of nature are independent waves without rest masses, and their speeds are constant in a vacuum, just like light. b. Light or electromagnetic waves and gravity are comparable in structures. Weak and strong interactions are similar in structures. c. Light and weak interaction have the same speed c_L with spin number +1 or –1. d. Gravity and strong interaction have the same speed c_G without spin. e. The primary particles, namely electrons, electron neutrinos, and dark neutrinos in this paper, are made by the above four waves. We can find and describe some fundamental characteristics of the primary particles (e.g., their sizes, energies, and interactions) and introduce new attractive results from them (e.g., the source of the Pauli exclusion principle, the solution to the Einstein-Podolsky-Rosen paradox, and c_G slightly faster than c_L).

This article presents a concise survey of basic discrete and semi-discrete nonlinear models which produce two- and three-dimensional (2D and 3D) solitons, and a summary of main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ⁽²⁾) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of basic species of multidimensional discrete modes, including fundamental and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

Bosons are particles that can occupy the same quantum state. Identical classical particles are considered distinguishable, but with bosons this is no longer the case. With bosons 1 and 2 in states α and β, the compound state function, ΨS=(1/2)Ψα(1)Ψβ(2)+Ψβ(1)Ψα(2), does not change when the particles are interchanged, i.e., there is one state where classically there would be two. This leads to boson statistics, which is different from Boltzmann statistics in that it favors putting more particles in the same state. For a sufficiently low temperature, it is possible that all bosons aggregate in the ground state where they effectively form a single megaparticle. We cover boson statistics and show how and why Bose-Einstein condensation can occur. We also show how growing networks like the WWW, the economy, or citation networks in scientific literature can follow boson statistics. Analyses of Bose-Einstein condensation have generally assumed a bath with a temperature, i.e., a thermal equilibrium where random collisions lead to a Gaussian-noise-term. However, many setups in physics involve conversion or transport of energy, i.e., nonequilibrium. Nonequilibrium noise is commonly characterized by the frequent occurrence of large kicks, i.e., outliers. We model this by implementing α-stable noise. No temperature exists in that case. We find that Bose-Einstein condensation is still theoretically possible, but probably much harder to engineer. Social and economic traffic is also often best modeled as nonequilibrium and our results may be significant in these contexts.

Albert Einstein, shortly after publishing his General Relativity Theory (GRT) applied it to the entire universe in a paper of 1917. Einstein assumed that such a universe was static in time and possessed a uniform distribution of matter on the largest scales, obtaining a static and finite universe of spherical spatial curvature of radius R. Although this model was refuted by Edwin Hubble's discovery of the expansion of the universe, it is still often studied as a theoretical framework for some problems, such as the twin paradox. This paper will show that Einstein's static universe model leads to a privileged frame of reference, so that any observer moving at the speed v will be able to measure speeds of light other than c depending on the direction of beam transmission. The above will refute the validity of the application to this closed and static universe of the Special Relativity Theory (SRT) proposed by Einstein in 1905 in his article . In addition, a new synchronization convention and new coordinate transformations will be deduced, the "generic" transformations, which will replace those of Lorentz. Finally, the twin paradox in this universe will be solved by making use of them.

This paper introduces a Unified Field Theory through the generalization of General Relativity, following the methodology outlined by Einstein for incorporating complex metrics in the pursuit of a comprehensive Unified Field Theory.

Assessment of the environmental impact of organic chemicals has become an important subject in chemical science. Efficient quantitative descriptors of their impact are their partition coefficients logPow, logKoa and logKaw. We present a group-additivity method that has proven its versatility for the reliable prediction of many other molecular descriptors for the calculation of the first two partition coefficients and indirectly of the third with high dependability. Based on the experimental logPow data of 3332 molecules and the experimental logKoa data of 1900 molecules at 298.15K the respective partition coefficients have been calculated with cross-validated standard deviations of only 0.42 and 0.48 log units and a goodness of fit Q^2 of 0.9599 and 0.9717, respectively, in a range of ca. 17 log units for both descriptors. The third partition coefficient logKaw has been derived from the calculated values of the former two descriptors and compared with the experimentally determined logKaw values of 1937 molecules, yielding a standard deviation of 0.67 log units and a correlation coefficient R^2 of 0.9467. This approach enabled the quick calculation of 29462 logPow, 27069 logKoa and 26220 logKaw values for the more than 37100 molecules of ChemBrain's database available to the public.

We propose a new theory beyond the standard model of elementary-particle physics. Employing the concept of a quantized spacetime, our theory demonstrates that the zero-point energy of the vacuum alone is sufficient to create all the fields, including gravity, the static electromagnetic field, and the weak and strong interactions. No serious undetermined parameters are assumed. Furthermore, the relations between the forces at the quantum-mechanics level is made clear. Using these relations, we quantize Einstein’s gravitational equation: Beginning with the zero-point energy of the vacuum, and after quantizing Newtonian gravity equation, we combine the energies of a static electromagnetic field and gravity in a quantum spacetime. Applying these results to the Einstein gravity equation, we substitute the energy density derived from the zero-point energy in addition to redefining differentials in a quantized spacetime. This is how we derive the quantized Einstein gravitational equation without assuming the existence of macroscopic masses. For the weak interaction, by considering plane-wave electron and the zero-point energy, we obtain a wavefunction that represents a β collapse. In this process, from a different point of view than Weinberg-Salam theory, we derive the masses of the W and Z bosons and the neutrino, and we calculate the radius and lifetime of the neutron. For the strong interaction, we previously reported an analytical theory for calculating the mass of a proton by providing a specific linear attractive potential obtained from the zero-point energy, which agrees well with the measurements. In the present study, we further calculate the strong interaction between two nucleons, i.e., the mass of the pi-meson. The resulting calculated quantities agree with the measurements, which verifies our proposed theory.

Snap-fit is a commonly used jointing/connention mechanism, and its easy installation and difficult removal are the result of the coordinated interaction between friction, geometric shape, and elasticity. This paper presents a detailed study on the assembly/disassembly forces of thin-walled torus snap-fit through finite element simulation, experimental testing, and data fitting of approximate analytical solutions. The research reveals that the non-zero Gaussian curvature of the torus has a significant impact on the mechanical performance of the torus snap fit. The findings in this study are of great significance for future design of high-performance structural connections.

For massive multiple-input multiple-output (MIMO) communications, the minimum mean square error (MMSE) scheme provides close to optimal recognition but involves inverting the high-dimensional matrix. A Gauss-Seidel (GS) detector based on conjugate gradient and Jacobi iteration (CJ) joint processing is introduced to address this problem. Firstly, the signal is initialized with the best of the three initialization regimes for faster algorithm convergence. Secondly, the signal is processed together with CJ. Finally, the pre-processed result is transferred to the GS detector. The simulation results indicate that the proposed iterative algorithm has a lower BER performance than the GS and improved iterative scheme based on GS in channels with different correlation levels.

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators.

Structure and reversibility of cross-link junctions play pivotal roles in deter- mining the nature of thermoreversible gelation and dynamic mechanical prop- erties of the produced polymer networks. We attempt to explore new types of sol–gel transitions with mechanical sharpness by allowing cross-links to grow without upper bound. We consider thermoreversible gelation of the primary molecules R{Af} carrying the number f of low molecular weight functional groups (gelators) A. Gelators A are assumed to form supramolecular assemblies. Some examples are: telechelic polymers (f = 2) carrying π–π stacking benzene derivatives at their both ends, trifunctional star molecules (f = 3) bearing mul- tiple hydrogen-bonding gelators. The sol–gel transition of the primary molecules becomes sharper with the cooperativity parameter of the stepwise linear growth of the cross-links. There is a polymerization transition (crossover without singu- larity) of the junctions in the postgel region after the gel point is passed. If the gelator A tends to form supramolecular rings competitively with linear chains, there is another phase transition in the deep postgel region where the average molecular weight of the rings becomes infinite (Bose-Einstein condensation of rings). As a typical example of binary cross-links where gelators A and B form mixed junctions, we specifically consider metal-coordinated binding of ligands A by metal ions B. Two types of multi-nuclear supramolecular complexes are studied: (i) linear stacking (ladder) of the sandwich A2B units, (ii) linear train of egg-box A4B units. The average molecular weight, the gel fraction, the av- erage length of the cross-link junctions are calculated for all of these models as functions of the functionality f, the concentration of the solute molecules, and temperature. Potential candidates for the realization of these new types of thermoreversible gelation are discussed.

This research focuses on exploring gravitational lensing of the wormhole in Einstein-bumblebee gravity with an antisymmetric tensor. The Gibbons and Werner technique based on the Gauss-Bonnet theorem is utilized to calculate the bending angle of light. The effects of non-plasma and plasma medium on the bending angles are investigated. Furthermore, we examine the deflection angle $\Tilde{\alpha}$ in relation to the impact parameter $\sigma$ and minimal radius $r_{0}$ in both non-plasma and plasma mediums. Our findings indicate that the deflection angle is positively correlated with $r_{0}$, meaning that larger values of $r_{0}$ result in larger deflection angles and smaller values of $r_{0}$ result in smaller deflection angles. On the other hand, the deflection angle $\Tilde{\alpha}$ is inversely related to the impact parameter $\sigma$.

: The silicon single crystals for semiconductor application is usually grown by Czochralski (CZ) method. This paper researches 300mm silicon Czochralski (CZ) crystal growth with CUSP magnetic field for IGBTs substrate application. The different positions of Zero-Gauss plane (ZGP) under CUSP magnetic field are simulated and compared to numerical analysis, investigated melt convection, melt flow velocity near to quartz crucible wall, diffusion boundary layer and effect of initial oxygen concentration in the silicon crystal, and the shape of solid/liquid interface was discussed. The results show that the change of the ZGP of the CMF mainly affects the convection in the melt, which leads to the difference of the thickness of the boundary layer near to the wall of the quartz crucible, and was found to be the key to reduce the oxygen dissolution from the crucible wall and oxygen diffuse into the crystal, along with the differences in the shape of the crystal-melt interface. In addition, we have carried out actual industrial single crystal production under the three configurations. The results show that the experimental data of oxygen content and shape of the crystal-melt interfaces in silicon crystal are consistent with the numerical results.

Coronavirus disease 2019 (COVID-19) is a high contagious respiratory infectious disease that has afiected millions of people worldwide. Initially, basic public health measures were implemented to control specially the spread of such virus. However, vaccination has emerged as a highly efiective strategy in combating COVID-19 and reducing its transmission. Several efiective and safe vaccines have been approved to prevent the inadvertent spread of the disease. In this study, a modeling approach is used to analyze the impact of these vaccines on the dynamics of COVID-19. By applying a higher-order numerical method, the model is solved based on reported cases in Pakistan. A spectral method is employed for the numerical solution, and the model is simulated to assess the efiects of vaccination. The Next-generation method is used to calculate the threshold quantity, known as R0, which indicates the potential for disease transmission. The study also includes a detailed stability analysis, examining the invariance properties of the model solution and discussing equilibrium points and their stability in disease-free and endemic states. Furthermore, the study presents graphical representations of the influence of special parameters on the dynamics of the pandemic.

In applied mathematics, statistics, operation research, physics, and engineering mathematics, confluent representations of hypergeometric functions in one and two variables are known to exist, and their occurrence in a variety of applications is also well recognised. In this article, we intend to present a new derivation of the extended Watson summation theorem for the Kim et al. given series 4F3. We assessed four attractive integrals involving generalized hypergeometric function as an application. With a few particular cases, this note will come to an end. In the results given above, symmetry appears on its own.

In this investigation, we explore the existence and intriguing features of matter wave positons in a nonautonomous one-dimensional Bose-Einstein condensate (BEC) system with attractive interatomic interactions. We focus on the Gross-Pitaevskii (GP) equation/nonlinear Schrödinger (NLS)-type equation with time-modulated nonlinearity and trap potential, governing nonlinear wave propagation in the BEC. Our approach involves constructing second- and third-order matter wave positons using a similarity transformation technique. We also identify the constraints on the time-modulated system parameters that give rise to these nonlinear localized profiles. The study considers three distinct forms of modulated nonlinearities: (i) kink-like, (ii) localized or -like, and (iii) periodic. By varying the parameters associated with the nonlinearity strengths, we observe a rich variety of evolution behaviors in the matter wave positon profiles. These behaviors include stretching, curving, oscillating, breathing, collapsing, amplification, and suppression. Our comprehensive studies shed light on the intricate dynamics of matter wave positons in BECs, providing valuable insights into their behavior and characteristics in the presence of time-modulated nonlinearity and trap potential effects.

In this paper, we introduce as a pedagogical strategy an internal division-free, straightforward, and symmetrically progressing algorithm in manually computing matrix inverse and solving systems of linear equations by revisiting the application of elementary row operations in the Gauss-Jordan reduction method and connecting it to the determinant method. The proposed cross-multiplication-flip (CMF) algorithm employs cross-multiplication similar to the butterfly movement in computing determinants as a strategic application of elementary row operations to efficiently reduce the rows and then applies flipping of rows and entries to put an upper triangular matrix into lower triangular form to continue the reduction process.

We investigate the evolution of gravitational waves through discontinuous evolution (transition) of the Hubble expansion rate H(z) at a sudden cosmological singularity which may be due to a transition of the value of the gravitational constant. We find the evolution of the scale factor and the gravitational wave waveform through the singularity by imposing the proper boundary conditions. We also use existing cosmological data and mock data of future gravitational wave experiments (the ET) to impose current and anticipated constraints on the magnitude of such a transition. We show that mock data of the Einstein Telescope can reduce the uncertainties by up to a factor of 3 depending on the cosmological parameter considered.

The paper discusses the 2022 Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravitation as belonging to the newly established quantum information science. Entanglement, involving non-Hermitian operators for its rigorous description, non-unitarity as well as nonlocal and superluminal physical signals “spookily” (by Einstein’s flowery epithet) synchronizing and transferring some nonzero action at a distance, can be considered to be quantum gravity so that its local counterpart to be Einstein’s gravitation according to general relativity therefore pioneering an alternative pathway to quantum gravitation different from the “secondary quantization” of the Standard model. So, the experiments of entanglement once they have been awarded by the Nobel Prize launch particularly the relevant theory of quantum gravitation grounded on “quantum information science” thus granted to be nonclassical quantum mechanics in the shared framework of the generalized quantum mechanics obeying rather quantum-information conservation than only energy conservation. The concept of “dark phase” of the universe naturally linked to the very well confirmed “dark matter” and “dark energy” and opposed to its “light phase” inherent to classical quantum mechanics and the Standard model obeys quantum-information conservation, after which reversible causality or the mutual transformation of energy and information are valid. The mythical Big Bang after which energy conservation holds universally is to be replaced by an omnipresent and omnitemporal medium of decoherence of the dark and nonlocal phase into the light and local phase. The former is only an integral image of the latter and borrowed in fact rather from religion than from science. Physical, methodological and proper philosophical conclusions follow from that paradigm shift heralded by the 2022 Nobel Prize in physics. For example, the scientific theory of thinking should originate from the dark phase of the universe, as well: probably only approximately modeled by neural networks physically belonging to the light phase thoroughly. A few crucial philosophical sequences follow from the break of Pauli’s paradigm: (1) the establishment of the “dark” phase of the universe as opposed to its “light” phase, only to which the Cartesian dichotomy of “body” and “mind” is valid; (2) quantum information conservation as relevant to the dark phase, furthermore generalizing energy conservation as to its light phase, productively allowing for physical entities to appear “ex nihilo”, i.e., from the dark phase, in which energy and time are yet inseparable from each other; (3) reversible causality as inherent to the dark phase; (4) the interpretation of gravitation only mathematically: as an interpretation of the incompleteness of finiteness to infinity, for example, following the Gödel dichotomy (“either contradiction or incompleteness”) about the relation of arithmetic to set theory; (5) the restriction of the concept of hierarchy only to the light phase; (6) the commensurability of both physical extremes of a quantum and the universe as a whole in the dark phase obeying quantum information conservation and akin to Nicholas of Cusa’s philosophical and theological worldview.

Gauss quadrature integral approximation is extended to include integrals with a measure consisting of a continuous as well as a discrete component. That is, we give an approximation for the integral of a function plus its sum over a discrete weighted set.

Spherically symmetric solution in 4D Einstein--Gauss--Bonnet gravity coupled to modified logarithmic nonlinear electrodynamics (ModLogNED) is found. This solution at infinity possesses the charged black hole Reissner--Nordstr\"{o}m behavior. We study the black hole thermodynamics, entropy, shadow, energy emission rate and quasinormal modes. It was shown that black holes can possess the phase transitions and at some range of event horizon radii black holes are stable. The entropy has the logarithmic correction to the area law. The shadow radii were calculated for variety of parameters. We found that there is a peak of the black hole energy emission rate. The real and imaginary parts of the quasinormal modes frequencies were calculated. The energy conditions of ModLogNED are investigated.

In this article key results in general relativity are studied and the dynamics of quantum fields in curved spacetime is reviewed. It has been shown geometrically how dark energy breaks strong energy condition. We study tan-hyperbolic inflation for an open FRWL universe and show that over half and full period scalar field remains in it's initial state.

Spacetime torsion is known to be highly suppressed at the end of inflation, called preheating. Of course this fact does not avoid that metric could affect the cosmic dynamos at preheating phase as was showed by Bassett et al, in the general relativity (GR) case. In this paper, is to show that a torsionful magnetogenesis in QED effective lagrangean, drives either a torsion damping or an amplification mechanism or dynamo effect, depending upon torsion chirality. The present extension of Basset et al theory yields a new magnetic field expression $B\sim{a^{(1\pm{\beta})}}$, obtained from dynamo equation in QED. Here a cosmic factor ${\beta}=g_{T}{\eta}k$ is present. In a second example we find Higgs inlationary fields in Einstein-Cartan gravity thick domain walls (DWs). Recently a moodified Einstein-Cartan gravity was given by M Shaposhnikov et al [PRL (2020)] to obtain higgs like inflatons as a portal to dark energy.

This paper is devoted to compute the weak deflection angle for Kalb-Ramond traversable wormhole solution in plasma and dark matter mediums by using the method of Gibbons and Werner. To acquire our results, we evaluate Gaussian optical curvature by utilizing the Gauss-Bonnet theorem in the weak field limits. We also investigate the graphical influence of deflection angle $\tilde{\alpha}$ with respect to the impact parameter $\sigma$ and minimal radius $r_0$ in plasma medium. Moreover, we derive the deflection angle by using different method known as Keeton and Petters method. We also examine that if we remove the effects of plasma and dark matter, the results become identical to that of non-plasma case.

In a continuation and extension of an earlier publication, the calculation of the refractivity and polarizability of organic molecules at standard conditions is presented, applying a commonly applicable computer algorithm based on an atom-group additivity method, where the molecules are broken down into their constituting atoms, these again being further characterized by their immediate neighbor atoms. The calculation of their group contributions, carried out by means of a fast Gauss–Seidel fitting calculus, used the experimental data of 5988 molecules from literature. An immediate subsequent ten-fold cross-validation test confirmed the extraordinary accuracy of the prediction of the molar refractivity, indicated by a correlation coefficient R^2 and a cross-validated analog Q^2 of 0.9997, a standard deviation σ of 0.38, a cross-validated analog S of 0.41, and a mean absolute deviation of 0.76%. The high reliability of the predictions has been exemplified with three classes of molecules: ionic liquids, silicon- and boron-containing compounds. The corresponding molecular polarizabilities have been calculated indirectly from the refractivity using the inverse Lorentz-Lorenz relation. In addition, it could be shown that there is a close relationship between the "true" volume and the refractivity of a molecule, revealing an excellent correlation coefficient R^2 of 0.9645 and a mean absolute deviation of 7.53%.

Nonlinear electrodynamics is known as the generalizations of Maxwell electrodynamics at strong fields and presents interesting features such as curing the classical divergences present in the linear theory when coupled to general relativity. In this paper, we consider the asymptotically flat Reissner-Nordstr\"om black hole solution with higher-order magnetic correction in Einstein-nonlinear-Maxwell fields. We study the effect of the magnetic charge parameters on the black hole, viz. weak deflection angle of photons and massive particles using Gauss-bonnet theorem. Moreover, we apply the Keeton-Petters formalism to confirm our results of the weak deflection angle. Apart from vacuum, their influence in the presence of different media such as plasma and dark matter are probed as well. Finally, We examine the black hole shadow cast using the null-geodesics method and investigate its spherically in-falling thin accretion disk. Our inferences show how the magnetic charge parameter $p$ affects the other physical quantities; so, we impose some constraints on this parameter using the observations from the Event Horizon Telescope.

In this work, we study gravitational lensing in the weak field limits and the shadow by charged black holes in non-linear electrodynamics corrections. To find the deflection angle in vacuum (non-plasma) up to the leading order terms, we compute the optical Gaussian curvature from optical metric and utilize the Gauss-Bonnet theorem by applying Gibbons and Werner’s technique. Also, we derive the bending angle in plasma and dark matter mediums and observe that the bending angle increases by increasing the effects of these mediums. Further, in vacuum and plasma mediums, we investigate the graphical behavior of the bending angle with respect to the impact parameter u and notice that the bending angle exponentially decreases. Moreover, we calculate the Hawking temperature using the Gauss-Bonnet theorem and compare it with a standard method of computing the Hawking temperature. Furthermore, we investigate the bound of the greybody factor and graphically examine that bound converges to the 1. We relate our obtained results with the results of black holes given in the literature. Finally, we have considered exploring the effect of NLED, plasma, and dark matter on the black hole’s shadow radius to broaden the study’s scope. Results for the shadow indicate that the three parameters give different deviations to the shadow radius. Interestingly, while plasma affects both the photonsphere and shadow, dark matter only influences the shadow.

In this paper, we study the deflection angle for wormhole-like static aether solution by using Gibbons and Werner technique in non-plasma, plasma and dark matter mediums. For this purpose, we use optical spacetime geometry to calculate the Gaussian optical curvature, then implement the Gauss-Bonnet theorem in weak field limits. Moreover, we compute the deflection angle by using a technique known as Keeton and Petters technique. Furthermore, we analyze the graphical behaviour of the bending angle ψ with respect to the impact parameter b, mass m as integration constant and parameter q in non-plasma and plasma mediums. We examine that deflection angle is exponentially increasing as direct with charge. Also, we observe that for small values of b, ψ increases and for large values of b the angle deceases. We also considered an analysis to the shadow cast of the wormhole relative to an observer at various locations. Comparing it the the Schwarzschild shadow, shadow cast is possible for wormhole as r<2m. At r>2m, the Schwarzschild is larger. As r → ∞, we have seen that the behavior of the shadow, as well as the weak deflection angle, approaches that of the Schwarzschild black hole. Overall, the effect of plasma tends to decrease the value of the observables due to the wormhole geometry.

In this paper, we study the weak deflection angle using Gauss-Bonnet theorem and bounding greybody factor for electric and magnetic black holes in the background of nonlinear electrodynamics. Using Gibbons and Werner's approach, first we acquire the Gaussian optical curvature to use in Gauss-Bonnet theorem and calculate the bending angle for spherically symmetric electric and magnetic black holes in both non-plasma and plasma mediums in the weak field limits. Later, we calculate the rigorous bounds of the greybody factor for the given black holes. Furthermore, we look into the graphical behaviour of bending angles and greybody bounds at some specific values of multiple parameters as well as black holes charges. It is to be mention here that all the results for the electric and magnetic charged black holes solutions reduce into the Schwarzschild black hole solution in the absence of the black holes charges.

In this work, we examine the deflection angle of black hole in effective loop quantum gravity in non-plasma medium via the geometrical technique of Gibbons and Werner in weak field limits. For this, we attain the optical metric and calculate the Gaussian optical curvature and then we apply the Gauss-Bonnet theorem. We also study the influence of the plasma and dark matter mediums on the deflection angle. Further, we obtain the deflection angle by using Keeton and Petters method. We also calculate the Hawking temperature via Gauss-Bonnet theorem. In addition, we determine the fermionic greybody bounds. Moreover, we discuss the graphical behaviour of the bending angle and bounds on the greybody factor. We also examine that the results obtained for the black hole in effective loop quantum gravity are reduces to the Schwarzschild black hole solutions when dimensionless non-negative parameter $A_{\lambda}=0$.

One of the solutions of the Einstein equations, called McVittie solution, signifying a black hole embedded by the dynamic spacetime is studied. In the stationary spacetime the Mcvittie metric becomes the Schwarzschild-de Sitter metric (SdS). The geodesic of a freely falling test particle towards the black hole is examined in the SdS spacetime. It is found that unlike Schwarzschild case the potential of such particle becomes maximum at a point where it eventually stops to follow an unstable circular motion and then resumes its motion towards black hole center. It is shown that an observer or system of particles is spaghettified near the black hole singularity in the SdS spacetime. The dynamic of the universe in the framework of McVittie metric, being a generalized time dependent SdS solution, is represented in terms of that point, called stationary or turning point. The motion of the stationary point is studied in various regimes of the expanding universe and the possible outcomes are discussed in brief.

Simulations based on Supernova (SN) observations predict several galactic SN explosions (SNe) occur every century. Unlike SNes within the Interstellar Medium (ISM) where ambient gas generally absorbs blast waves within a million years, SNes occurring in a rarified environment outside of the (ISM) generate blast waves which remain in a high velocity free expansion phase for more extended periods. The SN blast wave forms an expanding spherical shell and when multiple blast waves intersect, the overlapping region naturally takes the form of a ring, an arc, or an Einstein Cross structure. The analysis shows the high velocity plasma establishes a medium with permeability which drives the index of refraction greater than 1. As a result, when a shock discontinuity forms in the overlapping region, light is reflected from the host galaxy which exposes the intersecting blast wave regions. The expanding shells are shown to induce an achromatic redshift to the reflected light consistent with those measured for gravitational lenses. Further, it is shown that a Hubble equation for a blast wave around the Milky Way Galaxy can be parameterized to align with measured redshifts of extragalactic light fields over a wide range of distances.

In this study, we present a numerical method for solving two--dimensional space--time fractional partial differential equations (FPDEs), where the solutions of the FPDEs are expanded in terms of the shifted Chebyshev polynomials. The numerical approximations are evaluated at the Chebyshev-Gauss-Lobatto points. In the case when the FPDE is nonlinear, we employ a Newton-Raphson approach to linearize the equation. Both the linear and nonlinear cases lead to a consistent system of linear algebraic equations. The scheme is tested on selected FPDEs and the numerical results show that the proposed numerical scheme is accurate and computationally efficient in terms of CPU times. To establish the accuracy of the method, we also present an error analysis which shows the convergence of the numerical method. These positive attributes make the proposed method a good approach for solving two--dimensional fractional partial differential equations with both space and time fractional orders.

Considerable efforts have been devoted to modifying gravity, which aim to elucidate the possible existence or nature of dark matter and dark energy, achieve a better description of observation data, verify theoretical restrictions in the strong curvature regime and to formulate quantum gravity. In addition, despite the enormous success of the quantum field theory, the framework requires the so-called renormalization techniques and breaks down at high energies. Recently, the Planck Legacy 2018 release has confirmed the presence of an enhanced lensing amplitude in the cosmic microwave background power spectra, which prefers a positively curved early Universe with a confidence level greater than 99%. This study considers the implied positive curvature of the early Universe as the curvature of ‘the background or the 4D conformal bulk’ and distinguishes it from the localized curvature that is induced into the bulk by the presence of comparably smaller celestial objects that are regarded as ‘4D relativistic cloud-worlds’. To consider the interaction between the bulk and cloud-worlds, this paper presents interaction field equations in terms of the brane-world modified gravity counting for the bulk conformal curvature and the boundary terms, which could remove the singularities and satisfy a conformal invariance theory. Similarly, the quantum fields and clouds are regarded as ‘4D relativistic branes’ embedded in vacuum energy of a field strength reliant on the background curvature due to gravity. A visualization of the evolution of the 4D relativistic cloud-worlds over the conformal space-time of the 4D bulk is presented.

This paper results from our investigation into novel means of electromagnetic propulsion. It requires the basis of our claims to be put on a sound theoretical footing regarding the purported momentum exchange with the electromagnetic field. One of these concerns is the huge discrepancy between the energy density of the Zeropoint and its purported manifestation as the Cosmological Constant. Here we state that it is manifestly wrong to introduce the zeropoint at zero order into the stress-energy tensor, because it is something which describes zero particle count. As a fluctuation, it belongs in a higher order Taylor expansion in frequency of the stress-energy tensor. Furthermore in the 3^rd order in the Einstein constant our procedure is some 9 orders of magnitude too small. We make up this difference by suggesting that vacuum energy is much higher still and that more degrees of freedom exist in physics beyond the Standard Model or that there is interaction energy between the modes.

Potential dependent special relativity and Gauss's law for the electric field have been used for gravity by assuming vacuum energy to be generated when the energy is a minimum useful expression for vacuum energy has been found. This expression shows that elementary particles are generated by gravity vacuum filling their hollow balls; using Schrödinger equation for spherically symmetric particles vacuum energy is quantized. Treating mass as vibrating spheres thus solving Schrödinger, coordinate harmonic oscillator energy relation has been found.

Mass plays a strange multiple role in classical physics. This results in a difference between gravity and all other forces - a difference that stood at the beginning of Einstein's development of his general theory of relativity. The equivalence principle (EP) deals with homogenious gravitational fields, which, in fact, don‘t exist in nature. There is only an approximation for this field in Einstein-Lift possible for local situations. Nevertheless this EP can be true, because in classical formal binary logic there can be formulated a true conclusion from a wrong premise or assumption.

In this paper, we examine the weak deflection angle and greybody factor of magnetized regular black hole. We implement the Gauss-Bonnet theorem on magnetized regular black hole to get the deflection angle. Moreover, we analyze the influence of plasma and non-plasma mediums on deflection angle of magnetized regular black hole. We observe the graphical behaviour of plasma and non-plasma mediums on deflection angle of magnetized regular black hole. Lastly, we study the rigorous bound phenomenon of the greybody factor of magnetized regular black hole. For this purpose we calculate greybody factor results and analyze the graphical behaviour of greybody bound for the different values of the parameters.

The formulation used by most of the studies on an elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of a torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for the torus. In this paper, I will carry on my previous work [ B.H. Sun, Closed-form solution of axisymmetric slender elastic toroidal shells. J. of Engineering Mechanics, 136 (2010) 1281-1288.], and with the help of my own maple code, I am able to simulate some typical problems and free vibration of the torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. My investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. Regarding the free vibration of a torus, our analysis indicates that both initial in u and w direction must be included otherwise will cause big errors in eigenfrequency. One of the most intestine discovery is that the crowns of a torus are the turning point of the Gaussian curvature at the crown where the mechanics' response of inner and outer torus is almost separated.

The detection of Dark Matter is the greatest outstanding problem in modern cosmology. Several attempts have been taken for this without any remarkable success. To find out a suitable way of detection we need to understand its nature comprehensively. In the present article, a hypothesis is described considering Dark Matter as a normal matter. Its peculiar behavior is explained considering its existence in BEC state in the coolest part of the universe that makes it an electromagnetic insulator. Depending upon this hypothesis an experimental verification method is proposed.

After proposing a natural metric for the space in which particles spin which implements the principle of maximum frequency, E=hf is generalised and its inverse Fourier transform is calculated. As a necessary result, a metric is found for the space in which quantum particles spin, hence the possibility of explanation of correlation of spacelike-separated particles is opened up.

For a given material, different shapes correspond to different rigidities. In this paper, the radii of the oblique elliptic torus are formulated, a nonlinear displacement formulation is presented and numerical simulations are carried out for circular, normal elliptic, and oblique tori, respectively. Our investigation shows that both the deformation and the stress response of an elastic torus are sensitive to the radius ratio, and indicate that the analysis of a torus should be done by using the bending theory of shells rather than membrance theory. A numerical study demonstrates that the inner region of the torus is stiffer than the outer region due to the Gauss curvature. The study also shows that an elastic torus deforms in a very specific manner, as the strain and stress concentration in two very narrow regions around the top and bottom crowns. The desired rigidity can be achieved by adjusting the ratio of minor and major radii and the oblique angle.

In this project, our foremost intention is to analyze the angle of deflection of photon by NED black holes with many horizons in the context of non-linear electrodynamics. For the accomplishment of our intention at first we manipulated the optical metric of the desired black holes for the calculation of Gaussian curvature. After that, the angle of deflection in leading orders is attained from the desired black holes in weak field limit by using the famous Gauss-Bonnet theorem. Moreover, we evince the effect of plasma medium on the angle of deflection. At last, the graphical impact of the angle of deflection for NED black holes with many horizons is examined with respect to black hole charge and impact parameter in both the plasma and non plasma medium. In addition, we discuss the rigorous bound for grey body factor of the desired black hole and also observer its graphical behavior.

We explore the deflection angle in the framework of improved Schwarzschild Black hole utilizing the most advance geometrical path adopted by Gibbon-Werner. To investigate deflection angle of the photon ray by weak gravitational lensing for this black hole, we derive the optical curvature and perform the application of Gauss-Bonnet theorem on the optical metric. Moreover, we study the impacts of the plasma medium in context of the weak gravitational lensing in relate to this black hole. Further, we also study the graphical analysis of the deflection angle in both the plasma and non-plasma mediums. Also, we find the rigorous bound base upon the greybody factor for improved Schwarzschild black hole. A while later, we contrast our conclusions about deflection angle with the deflection angles of Schwarzschild black hole within plasma and non-plasma mediums.

The objective of this paper is to analyze the weak deflection angle of Einstein-Gauss-Bonnet gravity in the presence of plasma medium. To attain our results, we implement the Gibbons and Werner approach and use the Gauss-Bonnet theorem to Einstein gravity to acquire the resulting deflection angle of photon's ray in the weak field limit. Moreover, we illustrate the behavior of plasma medium and non-plasma mediums on the deflection of photon's ray in the framework of Einstein-Gauss-Bonnet gravity. Similarly, we observe the graphical influences of deflection angle on Einstein-Gauss-Bonnet gravity with the consideration of both plasma and non-plasma mediums. Later, we observe the rigorous bounds phenomenon of the greybody factor in contact with Einstein-Gauss-Bonnet gravity and calculate the outcomes, analyze graphically for specific values of parameters.

Classical methods for inverse problems are mainly based on regularization theory. In particular those which are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond, respectively, to the likelihood and prior probability models.

In this review, various researches on finding the bending angle of light deflected by a massive gravitating object which regard the Gauss-Bonnet theorem as the premise have been revised. Primarily, the Gibbons and Werner method is studied apropos of the gravitational lensing phenomenon in the weak field limits. Some exclusive instances are deliberated while calculating the deflection angle, beginning with the finite-distance corrections on non-asymptotically flat spacetimes. Effects of plasma medium is then inspected to observe its contribution to the deflection angle. Finally, the Jacobi metric is explored as an alternative method, only to arrive at similar results. All of the cases are probed in three constructs, one as a generic statement of explanation, one for black holes, and one for wormholes, so as to gain a perspective on every kind of influence.

In this article, we calculate the deflection angle of tidal charged black hole (TCBH) in weak field limits. First we obtain the Gaussian optical curvature and then apply the Gauss-Bonnet theorem on it. With the help of Gibbons-Werner method, we are able to calculate the light's deflection angle by TCBH in weak field limits. After calculating the deflection angle of light, we check the graphical behavior of TCBH. Moreover, we further find the light's deflection angle in the presence of plasma medium and also check the graphical behavior in the presence of plasma medium. Moreover, we investigate the shadow of TCBH.For calculating the shadow, we first find the null geodesics around the TCBH and then find its shadow radius. We also obtain TCBH's shadow in the plasma medium. Hence, we discuss the shadow of the TCBH using the $M87^{*}$ parameters announced by the Event Horizon Telescope.

This paper aims to present the basic assumptions for creation of social Fröhlich condensate and attract attention of other researchers (both from physics and socio-political science) to the problem of modelling of stability and order preservation in highly energetic society coupled with social energy bath of high temperature. The model of social Fröhlich condensation and its analysis are based on the mathematical formalism of quantum thermodynamics and field theory (applied outside of physics). The presented quantum-like model provides the consistent operational model of such complex socio-political phenomenon as Fröhlich condensation. The model of social Fröhlich condensation is heavily based on theory of open quantum systems. Its consistent elaboration needs additional efforts. Evidence of such phenomenon as social Fröhlich condensation is demonstrated by stability of modern informationally open societies Approaching the state of Fröhlich condensation is the powerful source of social stability. Understanding its informational structure and origin may help to stabilize the modern society. Application of the quantum-like model of Frhlich condensation in social and political sciences is really the novel and original approach to mathematical modeling of social stability in society exposed to powerful information radiation from mass-media and internet based sources.

In the same way as the realization of some of the famous gedanken experiments imagined by the founding fathers of quantum mechanics has recently led to the current renewal of the interpretation of quantum physics, it seems that the most recent progresses of observational astrophysics can be interpreted as the realization of some cosmological gedanken experiments such as the removal from the universe of the whole visible matter or the cosmic time travel leading to a new cosmological standard model. This standard model involves two dark components of the universe, dark energy and dark matter. Whereas dark energy is usually associated with the cosmological constant, we propose to explain dark matter as a pure QCD effect, namely a gluonic Bose Einstein condensate, following the transition from the quark gluon plasma phase to the colorless hadronic phase. Our approach not only allows us to assume a ratio Dark/Visible equal to 11/2 but also provides gluons and (anti-)quarks with an extra mass of vibrational nature. Such an interpretation would comfort the idea that, apart from the violation of the matter/antimatter symmetry satisfying the Sakharov’s conditions, the reconciliation of particle physics and cosmology needs not the recourse to any ad hoc fields, particles or hidden variables.

Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and time. The advances in trapping, cooling, and tuning the interparticle interactions in atomic Bose-Einstein condensates (BECs) make them excellent candidates for studying quantum turbulence. In this work, we investigate the decaying regime of quantum turbulence in a trapped BEC. Although much progress has been made in understanding quantum turbulence, other strategies are needed to overcome some intrinsic difficulties. We present an alternative way of investigating this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. One intrinsic difficulty related to these systems is that absorption images of BECs are projected to a plane, thus eliminating some of the information present in the original momentum distribution. We overcome this difficulty by exploring the symmetry of the cloud, which allows us to reconstruct the three-dimensional momentum distributions with the inverse Abel transform. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to visualize the time evolution of the turbulent state intuitively.

The Einstein’s Boxes paradox was developed by Einstein, de Broglie, Heisenberg, and others to demonstrate the incompleteness of the Copenhagen Formulation of quantum mechanics. I explain the paradox using the Copenhagen Formulation. I then show how a Time-Symmetric Formulation of quantum mechanics resolves the paradox in the way envisioned by Einstein and de Broglie. Finally, I describe an experiment that can distinguish between these two formulations.

The Einstein’s Boxes paradox was developed by Einstein, de Broglie, Heisenberg, and others to demonstrate the incompleteness of the Copenhagen Formulation of quantum mechanics. I explain the paradox using the Copenhagen Formulation. I then show how a Time-Symmetric Formulation of quantum mechanics resolves the paradox in the way envisioned by Einstein and de Broglie. Finally, I describe an experiment that can distinguish between these two formulations.

The main goal of this paper is to study the weak gravitational lensing by Horndeski black hole in weak field approximation. In order to do so, we exploit the Gibbons-Werner method to the optical geometry of Horndeski black hole and implement the Gauss-Bonnet theorem to accomplish the deflection angle of light in weak field region. Furthermore, we have endeavored to extend the scale of our work by comprising the impact of plasma medium on the deflection angle as properly. Later, the graphical influence of the deflection angle of photon on Horndeski black hole in plasma and non-plasma medium is examined.

Gedanken experiments illustrating exemplifications of the Landauer principle in the free falling Einstein elevator are treated. Double-well simplest information system embedded into the free falling elevator is addressed. Infinitesimal horizontal force applied to the particle m transfers it from position “0” to position “1”, emerging from the free falling double-well system confining mass m. When thermal noise is considered, the potential barrier of kBT should be surmounted for the erasing of one bit of information. Entropic forces arising in the free falling elevator are considered. The maximal change in the entropy of free-joint polymer chain attached to the free falling elevator is estimated as ΔSmax≅kB, and it is remarkably independent of the mass attached to the chain and the parameters of the chain itself. Free falling minimal Szilard engine is treated. The informational re-interpretation of the minimal Szilard process is shaped as follows: the energy kBTln2 necessary for erasing of 1 bit of information is spent for lifting up mass, whatever, is the value of this mass. Appropriate choice of frames enables elimination of gravity in the considered system; however elimination of the thermal noise (dissipation processes) by the same procedure is impossible.

The nonlinear deformation and stress analysis of a circular torus is a difficult undertaking due to its complicated topology and the variation of the Gauss curvature. A nonlinear deformation (only one term in strain is omitted) of Mindlin torus was formulated in terms of the generalized displacement, and a general Maple code was written for numerical simulations. Numerical investigations show that the results obtained by nonlinear Mindlin, linear Mindlin, nonlinear Kirchhoff-Love, and linear Kirchhoff-Love models are close to each other. The study further reveals that the linear Kirchhoff-Love modeling of the circular torus gives good accuracy and provides assurance that the nonlinear deformation and stress analysis (not dynamics) of a Mindlin torus can be replaced by a simpler formulation, such as a linear Kirchhoff-Love theory of the torus, which has not been reported in the literature.

We investigate the dynamics and stationary states of a semiconductor exciton-polariton condensate in a double well potential. We find that upon the population build up of the polaritons by above-threshold laser pumping, coherence relaxation due to the phase fluctuations of the polaritons drives the system into a stable fixed point corresponding to a self-organized PT-symmetric phase.

In this paper, we study light rays in a Kazakov-Solodukhin black hole. To this end, we use the optical geometry of the Kazakov-Solodukhin black hole within the Gauss-bonnet theorem. We first show the effect of the deformation parameter $a$ on the Gaussian optical curvature, and then we use the modern method popularized by Gibbons and Werner to calculate the weak deflection angle of light. Our calculations of deflection angle show how gravitational lensing is affected by the deformation parameter $a$. Moreover, we demonstrate the effect of a plasma medium on weak gravitational lensing by the Kazakov-Solodukhin black hole. We discuss that the increasing the deformation parameter $a$, will increase the weak deflection angle of the black hole. Our analysis also uncloak how one may find a observational evidence for a deformation parameter on the deflection angle.

We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlev\`e-Gullstrand, and Schwarzschild coordinates, and present both time-dependent and time-independent exact vacuum solutions. In particular, in the isotropic coordinates we find a class of exact static solutions characterized bya single parameter $c_{14}$ in closed forms, which satisfies all the current observational constraints of the theory, and reduces to the Schwarzschild vacuum black hole solution in the decoupling limit ($c_{14} = 0$). However, as long as $c_{14} \not= 0$, a marginally trapped throat with a finite non-zero radius always exists, and in one side of it the spacetime is asymptotically flat, while in the other side the spacetime becomes singular within a finite proper distance from the throat, although the geometric area is infinitely large at the singularity. Moreover, the singularity is a strong and spacetime curvature singularity, at which both of the Ricci and Kretschmann scalars become infinitely large.

It is introduced and studied para-Ricci-like solitons with potential Reeb vector field on almost paracontact almost paracomplex Riemannian manifolds. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field have been considered. It is proved a necessary and sufficient condition the manifold to admit a para-Ricci-like soliton which is the structure to be para-Einstein-like. Explicit examples are provided in support of the proven statements.

The unexploited unification of general relativity and quantum mechanics (QM) prevents the proper understanding of the micro- and macroscopic world. Here we put forward a mathematical approach that introduces the problem in terms of negative curvature manifolds. We suggest that the oscillatory dynamics described by wave functions might take place on hyperbolic continuous manifolds, standing for the counterpart of QM’s Hilbert spaces. We describe how the tenets of QM, such as the observable A, the autostates ψa and the Schrodinger equation for the temporal evolution of states, might work very well on a Poincaré disk equipped with rotational groups. This curvature-based approach to QM, combined with the noncommutativity formulated in the language of gyrovectors, leads to a mathematical framework that might be useful in the investigation of relativity/QM relationships. Furthermore, we introduce a topological theorem, termed the punctured balloon theorem (PBT), which states that an orientable genus-1 surface cannot encompass disjoint points. PBT suggests that hyperbolic QM manifolds must be of genus ≥ 1 before measuring and genus zero after measuring. We discuss the implications of PBT in gauge theories and in the physics of the black holes.

Shown is the derivation of Lorentz-Einstein k-factor in SRT as an amplitude-term of oscillation-differential equations of second order.This case is shown for classical Lorentz-factor as solution of an equation for undamped oscillation as well as the developed theorem as a second solution for advanced SRT of fourth order with an equation for damped oscillation-states.This advanced term allows a calculation for any velocities by real rest mass.Also accelerated coordinate -frames are discussed.

Atomtronics is a relatively new subfield of atomic physics that aims to realize the device behavior of electronic components in ultracold atom-optical systems. The fact that these systems are coherent makes them particularly interesting since, in addition to current, one can impart quantum states onto the current carriers themselves or perhaps perform quantum computational operations on them. After reviewing the fundamental ideas of this subfield, we report on the theoretical and experimental progress made towards developing externally-driven and closed loop devices. The functionality and potential applications for these atom analogs to electronic and spintronic systems is also discussed.

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation and we show that the trajectories of the particles are ellipses centered on the horizon of the events. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian and the computations are performed within the framework of special relativity. Some experimental consequences are discussed such as trajectory deviation, desynchronization of a falling clock and the Michelson interferometer. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the box where the interest is above all theoretical and pedagogical. The study helps the student to become familiar with the concepts of metric, coordinate velocity, horizon, and, to do the analogy with the black hole.

The catenary shells of revolution are widely used in constructions due to their unique mechanics' feature. However, no publications on this type of shells can be found in the literature. To have a better understanding of the deformation and stress of the catenary shells of revolution, we formulate the principal radii for two kinds of catenary shells of revolution and their displacement type governing equations. Numerical simulations are carried out based on both Reissner-Meissner mixed formulations and displacement formulations. Our investigations show that both deformation and stress response of elastic catenary shells of revolution are sensitive to its geometric parameter $c$, and reveal that the mechanics of the catenary shells of revolution does much better than the spherical shells. Two complete codes in Maple are provided.

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, a complex-form ordinary differential equation (ODE) for the small symmetrical deformation of an elastic torus is successfully transformed into the well-known Heun's ODE, whose exact solution is obtained in terms of Heun's functions. To overcome the computational difficulties of the complex-form ODE in dealing with boundary conditions, a real-form ODE system is proposed. A general code of numerical solution of the real-form ODE is written by using Maple. Some numerical studies are carried out and verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell.

The logarithmic correction to Bekenshtein$-$Hawking entropy in the framework of 4D Einstein - Gauss - Bonnet gravity coupled with nonlinear electrodynamics is obtained. We explore the black hole solution with the spherically symmetric metric. The logarithmic term in the entropy has a structure similar to the entropy correction in the semi-classical Einstein equations which mimics the quantum correction to the area low. The energy emission rate of black holes and energy conditions are studied. The quasinormal modes of a test scalar field are investigated. The gravitational lensing of light around BHs was studied. We calculated the deflection angle for some model parameters.

Chronology unprotected mechanisms are considered with a very low gravitational polarization to make the wormhole traversal with positive energy density everywhere. No need of exotic matter has been considered with the assumption of the Einstein-Dirac-Maxwell Fields, encountering above the non-zero stress-energy-momentum tensor through spacelike hypersurfaces by a hyperbolic coordinate shift.

The Gol'denveizer problem of a torus can be described as follows: a toroidal shell is loaded under axial forces and the outer and inner equators are loaded with opposite balanced forces. Gol'denveizer pointed out that the membrane theory of shells is unable to predict deformation in this problem, as it yields diverging stress near the crowns. Although the problem has been studied by Audoly and Pomeau (2002) with the membrane theory of shells, the problem is still far from resolved within the framework of bending theory of shells. In this paper, the bending theory of shells is applied to formulate the Gol'denveizer problem of a torus. To overcome the computational difficulties of the governing complex-form ordinary differential equation (ODE), the complex-form ODE is converted into a real-form ODE system. Several numerical studies are carried out and verified by finite-element analysis. Investigations reveal that the deformation and stress of an elastic torus are sensitive to the radius ratio, and the Gol'denveizer problem of a torus can only be fully understood based on the bending theory of shells.

The formulation used by the most of studies on an elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of the torus, application of those formulations has encountered great difficulty. It is highly demanded to have a displacement-type formulation for the torus. In this paper, I will simulate some typical problems and free vibration of the torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. My investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. Regarding the free vibration of the torus, our analysis indicates that both initial in u and w direction must be included otherwise will cause big errors in eigenfrequency.

A given problem in physics can be solved if it is well formulated. Well formulated means that it has a bijective correspondence to physical reality. Mass Gap Problem has no bijective correspondence with the physical reality and is that’s why not solvable mathematically. It can be solved in the frame of quantum mechanics by the formulation of the photon’s mass accordingly to the Planck-Einstein relation.

In this work, we explore a the different forms of a new type of modified gravity, namely f(φ) gravity. We construct the Big Rip type for the energy density and the curvature of the universe. We show that dark energy is a result of the transformation of the field φ mass (dark matter) to energy. In addition, we provide that Ω_{m}≈0,050, Ω_{DM}≈0,2, Ω_{DE}≈0,746, is in excellent agreement with observation data. We explore a generalized formalism of braneworld modified gravity. We also construct a new field equations, which generalize the Einstein field equations. We provide a relation between the extra dimension in 3-brane with the vacuum energy density. We show that the energy density of matter depends directly on the number of dimensions. We manage to find the value of the Gauss-Bonnet coupling α=1/4 which is a good agreement with the results in the literature, this correspondence creates a passage between f(R) gravity and Gauss-Bonnet gravity, this comparison leads to a number of bulk dimensions equal to D=10¹²¹+4.

A generalization of $\eta$-Ricci solitons is considered involving an additional metric and functions as soliton coefficients. The soliton potential is torse-forming and orthogonal to the contact distribution of the almost contact B-metric manifold. Then such a manifold can also be considered as an almost Einstein-like manifold, a generalization of an $\eta$-Einstein manifold with respect to both B-metrics and functions as coefficients. Necessary and sufficient conditions are found for a number of properties of the curvature tensor and its Ricci tensor of the studied manifolds. Finally, an explicit example of an arbitrary dimension is given and some of the results are illustrated.

In this paper, we found a new model for compact star with charged anisotropic matter distribution considering an extended version of the Chaplygin equation of state. We specify a particular form of the metric potential Z(x) that allows us to solve the Einstein-Maxwell field equations. The obtained model satisfies all physical properties expected in a realistic star such that the expressions for the radial pressure, energy density, metric coefficients, measure of anisotropy and the mass are fully well defined and are regular in the interior of star. The solution obtained in this work can have multiple applications in astrophysics and cosmology.

In this paper, by considering Einstein-Hilbert-Bumblebee (EHB) gravity around global monopole field, we derive exactly a black hole spacetime metric. To test the effect of global monopole field and bumblebee field, which causes the spontaneous Lorentz symmetry breaking, we calculate the weak deflection angle using the Gauss-Bonnet theorem.

An exact spherically symmetric and magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics (NED) is obtained. The NED Lagrangian is given by ${\cal L}_{NED} = -{\cal F}/(1+\sqrt[4]{2\beta{\cal F}})$, where ${\cal F}$ is the field invariant. We study the thermodynamics calculating the Hawking temperature and the heat capacity of the black hole. The phase transitions take place when the Hawking temperature has an extremum and the heat capacity is singular. We demonstrate that black holes are thermodynamically stable in some range of event horizon radii where the heat capacity is positive. The BH shadow radii are calculated. It is shown that when increasing the nonlinearity parameter $\beta$ the BH shadow radius is decreased.

Decoherence with recurrences appear in the dynamics of the one-body density matrix of an $F = 1$ spinor Bose-Einstein condensate, initially prepared in coherent states, in the presence of an external uniform magnetic field and within the single mode approximation. The phenomenon emerges as a many-body effect of the interplay of the quadratic Zeeman effect, that breaks the rotational symmetry, and the spin-spin interactions. By performing full quantum diagonalizations very accurate time evolution of large condensates are analyzed, leading to heuristic analytic expressions for the time dependence of the density matrix, in the weak and strong interacting regimes. We are able to find accurate analytical expressions for both the decoherence and the recurrence times, in terms of the number of atoms and strength parameters, that show remarkable differences depending on the strength of the spin-spin interactions. We discuss the nature of these limits in the light of the thermodynamic limit.

Black hole's quasinormal frequencies are basically the complex numbers which provide information about the relaxation of perturbations and depend on the characteristics of the spacetime and types of perturbations. In this paper, we evaluate the quasinormal modes of Hayward black hole in Einstein Gauss-Bonnet gravity, Hayward black hole in anti-de Sitter space (AdS) spacetime, and 4-dimensional black hole in Einstein-Lovelock gravity. By utilizing the WKB resonance technique, we examine the quasinormal modes frequencies $\omega$ by shifting the charge parameter $Q$ (it is also identified with the cosmological constant), circular harmonic index $l$, and mass of scalar field $m$. We also study the relaxation rate for those black holes and find out that the relaxation rate increases with increasing values of $Q$. We observe that real and imaginary components of the quasinormal modes are not linear functions as similar to Reisnner Nordstr\"{o}m-AdS. For large values of charge, quasinormal ringing becomes slower to settle down to thermal equilibrium and hence the frequency of the oscillation becomes smaller.

In this paper, first we use the optical metrics of black-bounce traversable wormholes to calculate the Gaussian curvature. Then we use the Gauss-Bonnet theorem to obtain the weak deflection angle of light from the black-bounce traversable wormholes. Then we investigate the effect of dark matter medium on weak deflection angle using the Gauss-Bonnet theorem. We show how weak deflection angle of wormhole is affected by the bounce parameter $a$. Using the Gauss-bonnet theorem for calculating weak deflection angle shows us that light bending can be thought as a global and topological effect.

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

Quantum turbulence deals with the phenomenon of turbulence in quantum fluids, such as superfluid helium and trapped Bose-Einstein condensates (BECs). Although much progress has been made in understanding quantum turbulence, several fundamental questions remain to be answered. In this work, we investigated the entropy of a trapped BEC in several regimes, including equilibrium, small excitations, the onset of turbulence, and a turbulent state. We considered the time evolution when the system is perturbed and let to evolve after the external excitation is turned off. We derived an expression for the entropy consistent with the accessible experimental data, that is, using the assumption that the momentum distribution is well-known. We related the excitation amplitude to different stages of the perturbed system, and we found distinct features of the entropy in each of them. In particular, we observed a sudden increase in the entropy following the establishment of a particle cascade. We argue that entropy and related quantities can be used to investigate and characterize quantum turbulence.

The principal objective of this project is to investigate the gravitational lensing by asymptotically flat black holes in the framework of Horndeski theory in weak field limits. To achieve this objective, we utilize the Gauss-Bonnet theorem to the optical geometry of asymptotically flat black holes and applying the Gibbons-Werner technique to achieve the deflection angle of photons in weak field limits. Subsequently, we manifest the influence of plasma medium on deflection of photons by asymptotically flat black holes in the context of Horndeski theory. We also examine the graphical impact of deflection angle on asymptotically flat black holes in the background of Horndeski theory in plasma as well as non-plasma medium.

General wisdom thinks that the central of blackholes are singular and featured by mass, charge and spin exclusively; the microstate reflected in the Bekenstein-Hawking entropy can be accounted for only in some quantum gravity. We challenge this wisdom with two exact solution families to the sourceful Einstein equation which describe dust ball with oscillatory inner structure and variety of mass profiles. We attribute the matter content's oscillation across the central point of the system to the forward scattering domination in high energy collisions induced by inter-gravitating acceleration and provide their Penrose-Carter diagram representation and quantum description briefly. Our solution family provides a very simple semi-classic picture for the micorstate definition of black holes.

We consider a four-dimensional Riemannian manifold M with an additional structure S, whose fourth power is minus identity. In a local coordinate system the components of the metric g and the structure S form skew-circulant matrices. Both structures S and g are compatible, such that an isometry is induced in every tangent space of M. By a special identity for the curvature tensor, generated by the Riemannian connection of g, we determine classes of Einstein and almost Einstein manifolds. For such manifolds we obtain propositions for the sectional curvatures of some characteristic 2-planes in a tangent space of M. We consider a Hermitian manifold associated with the studied manifold and find conditions for g, under which it is a K\"{a}hler manifold. We construct some examples of the considered manifolds on Lie groups.

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the symmetrical deformation equation of elastic toroidal shells is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The Gauss curvature of the elastic toroidal shells shows that the internal portion of the toroidal shells has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shells cells. Through numerical comparison study, the mechanics of elastic toroidal shells is sensitive to the radius ratio. By slightly adjustment of the ratio might get a desired high performance shell structure.

The Einstein-Lovelock theory contains an infinite series of corrections to the Einstein term with an increasing power of the curvature. It is well-known that for large black holes the lowest (Gauss-Bonnet) term is the dominant one, while for smaller black holes higher curvature corrections become important. We will show that if one is limited by positive values of the coupling constants, then the dynamical instability of black holes serves as an effective cut-off of influence of higher curvature corrections in the 4D Einstein-Lovelock approach: the higher is the order of the Lovelock term, the smaller is the maximal value of the coupling constant allowing for stability, so that effectively only a first few orders can deform the observable values seemingly. For negative values of coupling constants this is not so, and, despite some suppression of higher order terms also occurs due to the decreasing threshold values of the coupling constant, this does not lead to an noticeable opportunity to neglect higher order corrections. In the case a lot of orders of Lovelock theory are taken into account, so that the black-hole solution depends on a great number of coupling constants, we propose a compact description of it in terms of only two or three parameters encoding all the observable values.

In this work, we investigate the weak deflection angle of light from exact black hole within the non-linear electrodynamics. First we calculate the Gaussian optical curvature using the optical spacetime geometry. With the help of modern geometrical way popularized by Gibbons and Werner, we examine the deflection angle of light from exact black hole. For this desire, we determine the optical Gaussian curvature and execute the Gauss-Bonnet theorem on optical metric and calculate the leading terms of deflection angle in the weak limit approximation. Furthermore, we likewise study the plasma medium's effect on weak gravitational lensing by exact black hole. Hence we expose the effect of the non-linear electrodynamics on the deflection angle in the weak gravitational field.

In this paper, we use a new asymptotically flat and spherically symmetric solution in the generalized Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity to study the weak gravitational lensing and its shadow cast. To this end, we first compute the weak deflection angle of generalized ECKS black hole using the Gauss–Bonnet theorem in plasma medium and in vacuum. Next by using the Newman-Janis algorithm without complexification, we derive the rotating generalized ECKS black hole and in the sequel study its shadow. Then, we discuss the effect of the ECKS parameter on the shadow of the black hole and weak deflection angle. In short, the goal of this paper is to give contribution to the ECKS theory and look for evidences to understand how the ECKS parameter effects the gravitational lensing.

The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the weak gravitational deflection of null and time-like particles based on Gauss-Bonnet theorem. By this way, we obtain an expression of deflection angle and extend the study of deflection angle to asymptotically non-flat black hole spacetimes. Some black holes as lens are considered such as a static and spherically symmetric black hole in the conformal Weyl gravity and a Schwarzschild-like black hole in bumblebee gravity. Our results are consistent with the previous literature. In particular, we find that the connection between Gaussian curvature and the radius of a circular orbit greatly simplifies the calculation.

In this article, we demonstrate the weak gravitational lensing in the context of Bocharova-Bronnikove-Melnikov-Bekenstein (BBMB) black hole. To this desire, we derive the deflection angle of light in a plasma medium by BBMB black hole using the Gibbons and Werner method. First, we obtain the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle for spherically symmetric spacetime of BBMB black hole. Moreover, we also analyze the graphical behavior of deflection angle by BBMB black hole in the presence of plasma medium.

In this paper, we calculate the deflection angle of photon by Casimir wormhole in the weak field limit approximation. First we calculate Gaussian optical curvature with the help of optical spacetime geometry and so we use the Gauss-Bonnet theorem on the Gaussian optical metric. Then we find the deflection angle of photon by Casimir wormhole. Moreover, we calculate the photon's deflection angle in the presence of plasma medium and we also see the graphical nature of deflection angle in both cases. Second, we move towards the shadow of Casimir wormhole. After the observations of Event Horizon Telescope, the study of shadow become very important so that we plot the shapes of shadow of Casimir wormhole, and we calculate the photon geodesic around the Casimir wormhole.

In this article, we analyze the weak gravitational lensing in the context of Einstein-non-linear Maxwell-Yukawa black hole. To this desire, we derive the deflection angle of light by Einstein-non-linear Maxwell-Yukawa black hole using the Gibbons and Werner method. For this purpose, we obtain the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle of Einstein-non-linear Maxwell-Yukawa black hole. Moreover, we derive the deflection angle of light in the presence of plasma medium. We also analyze the graphical behavior of deflection angle by Einstein-non-linear Maxwell-Yukawa black hole in the presence of plasma as well as non-plasma medium.

Recent astronomical observations with respect to measurements in distant supernovas, cosmic microwave background and weak gravitational lensing confirm that the Universe is undergoing a phase of accelerated expansion and it has been proposed that this cosmological behavior is caused by a hypothetical dark energy which has a strong negative pressure that allows explain the expanding universe. Several theoretical ideas and models related dark the energy includes the cosmological constant, quintessence, Chaplygin gas, braneworld and tachyonic scalar fields. In this paper, we have obtained new relativistic stellar configurations considering an anisotropic fluid distribution with a charge distribution which could represents a potential model of a dark energy star. In order to investigate the effect of a quadratic equation of state in this anisotropic model we specify particular forms for the gravitational potential that allow solving the Einstein-Maxwell field equations. For these new solutions we checked that the radial pressure, metric coefficients, energy density, anisotropy factor, charge density , mass function are well defined and are regular in the interior of the star. The solutions found can be used in the development of dark energy stars models satisfying all physical acceptability conditions but the causality condition and strong energy condition are violated. We expect that these models have multiple applications in astrophysics and cosmology.

In this paper, we discuss the weak gravitational lensing in the context of stringy black holes. Initially, we examine the deflection angle of photon by charged stringy black hole. For this desire, we compute the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle for spherically balanced spacetime of stringy black hole. We also analyze the influence of plasma medium in the weak gravitational lensing for stringy black hole. Moreover, the graphical impact of coupling constant $\alpha$, impact parameter $b$ , black hole charge $Q$ on deflection angle by charged stringy black hole has been studied in plasma as well as non-plasma medium.