In this letter, instead of choosing the Einstein Rosen bridge between two black holes as in ER=EPR, we consider a wormhole between a black hole and a closed edge of the wormhole. We assume that information in a black hole travels through a wormhole, turns to mass (dark matter) in the closed region. This study is in contradiction with the existence of the white hole in our Universe. We replace the notion of the white hole with the massive closed region. We prove the metric of the closed region by the Hopf fibration, this new metric generalizes the $AdS_{5}$\ metric.

Is it possible to quantify in General Relativity, GR, the entropy generated by supermassive black holes, BHs, during its evaporation time, since the intrinsic Hawking radiation in the infinity that, although insignificant, is important in the effects on the thermal quantum atmosphere?The purpose was to develop a formula that allows us to measure the entropy generated during the evaporation time of different types of BHs of: i. remnant BH of the binary black holes’ merger, BBH: GW150914, GW151226 and LTV151012 detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO), and ii. Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman, and thus quantify in GR the “insignificant” quantum effects involved, in order to contribute to the validity of the generalized second law (GSL) that directly links the laws of black hole mechanics to the ordinary laws of thermodynamics, as a starting point for unifying quantum effects with GR. This formula could have some relationship with the detection of the shadow’s image of the event horizon of a BH.This formula was developed in dimensional analysis, using the constants of nature and the possible evaporation time of a black hole, to quantify the entropy generated during that time. The energy-stress tensor was calculated with the 4 metrics to obtain the material content and apply the proposed formula.The entropy of the evaporation time of BHs proved to be insignificant, its temperature is barely above absolute zero, however, the calculation of this type of entropy allows us to argue about the importance of the quantum effects of Hawking radiation mentioned by authors who have studied the quantum effects with arguments that are fundamentally based on the presence of the surrounding thermal atmosphere of the black hole.

Gravitational waves have been detected in the past few years from several transient events such as merging stellar mass black holes, binary neutron stars, etc. These waves have frequencies in a band ranging from a few hundred hertz to around a kilohertz to which LIGO type instruments are sensitive. LISA would be sensitive to much lower range of frequencies from SMBH mergers. Apart from these cataclysmic burst events, there are innumerable sources of radiation which are continuously emitting gravitational waves of all frequencies. These include a whole mass range of compact binary and isolated compact objects as well as close planetary stellar entities. In this work, quantitative estimates are made of the gravitational wave background produced in typical frequency ranges from such sources emitting over a Hubble time and the fluctuations in the h values measured in the usual devices. Also estimates are made of the high frequency thermal background gravitational radiation from hot stellar interiors and newly formed compact objects.

In this paper, we present a technique to unify the Reissner–Nordstr¨om metric and the Kerr–Newman metric. We construct a specifific model and calculate the entanglement entropy of black horizon. We are interested in the entangled particle and antiparticle spinning on the black hole horizon. The two Reissner-Nordstr¨om horizons r±, are the results of the rotation of several entangled particle-antiparticle on the real horizon. The energy absorbed by a black hole is transformed into a kinetic energy of the entangled particle-antiparticles. This study provides a new type of black hole metric. We show that the rotation of an entangled system of a particle and an antiparticle can create a extremal black hole. We also explore some of the implications of this point of view for the black hole entanglement.

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.

Various techniques to tackle the black hole information paradox have been proposed. A new way out to tackle the paradox is via the use of pseudo-density operator. This approach has successfully dealt the problem with a two-qubit entangle system for a single black hole. In this paper, we present the interaction with a binary black hole system by using an arrangement of the three-qubit system of Greenberger–Horne–Zeilinger (GHZ) state. We show that our results are in excellent agreement with the theoretical value. We have also studied the interaction between the two black holes by considering the correlation between the qubits in the binary black hole system. The results depict a complete agreement with the proposed model. In addition to the verification, we also propose how modern detection of gravitational waves can be used on our optical setup as an input source, thus bridging the gap with the gravitational wave’s observational resources in terms of studying black hole properties with respect to quantum information and entanglement.

The energy E takes the place of the gravitational mass m_G to produce gravity [1]. We wonder whether the inertial mass m_i in the inertial force is also replaced by E. The experiments to measure the inertial force and weight of a carrier are presented. Now we can test the principle of equivalence and study foundations of physics in condensed matter.

In this paper, we discuss optical properties of the topologically charged rotating black hole. We study the horizon, the photon region, the shadow of the black hole and other observables. The results show that in addition to the black hole spin parameter $a$, the other two parameters, five-dimensional mass parameter $\beta$ and electric charge $q$, are also found to affect the horzion, the photon region and the black hole shadow. In a certain range, with the increase of the three parameters, the horizon distance, shape of the photon region and the black hole shadow will all shrink. Moreover, with the increase of these three parameters, the distortion parameter $\delta_{s}$ gradually increases, while the peak of the black hole energy emission rate decreases.

This paper presents a new approach of eddy current methods for determining the size of the co-axial hole in the metallic circular disk. In recent decades, for the air-cored sensor probe, the impedance change due to the presence of an infinite metal plate can be calculated by the Dodd-Deeds model. However, in practical measurements, the sample cannot match with the condition required - ‘infinite’, thus the Dodd-Deeds model could not be applied to the disk with finite size and certainly not a co-axial hole in the center. In this paper, a dual-constraint analytical method is proposed. That is, the upper and lower limits of the integration are substituted with specific values instead of the original 0 and . Besides, it is found that, once the outer radius of the disk is fixed (i.e. the lower limit of integration is fixed), the upper limit reduces linearly as the size of the coaxial hole increases. Both the FEM simulation and experiments have been carried out to validate this method. The radius of the hole can be estimated based on the dual-constraint integration feature.

We consider rational nonlinear electrodynamics with the Lagrangian ${\cal L} = -{\cal F}/(1+2\beta{\cal F})$ (${\cal F}=(1/4)F_{\mu\nu}F^{\mu\nu}$ is the Lorentz-invariant), proposed in \cite{Krug2}, coupled to General Relativity. The effective geometry induced by nonlinear electrodynamics corrections are found. We determine shadow's size of regular non-rotating magnetic black holes and compare them with the shadow size of the super-massive M87* black hole imaged by the Event Horizon Telescope collaboration. Assuming that the black hole mass has a pure electromagnetic nature, we obtain the black hole magnetic charge. The size of the shadow obtained is very close to the shadow size of non-regular neutral Schwarzschild black holes. As a result, we can interpret the super-massive M87* black hole as a regular (without singularities) magnetized black hole.

The thermodynamics of black holes is discussed for the case, when the Newton constant G is not a constant, but is the thermodynamic variable. This gives for the first law of the Schwarzschild black hole thermodynamics: d S BH = − A d K + d M T BH , where the gravitational coupling K = 1 / 4 G , M is the black hole mass, A is the area of horizon, and T BH is Hawking temperature. From this first law it follows that the dimensionless quantity M 2 / K is the adiabatic invariant, which in principle can be quantized if to follow the Bekenstein conjecture. From the Euclidean action for the black hole it follows that K and A serve as dynamically conjugate variables. This allows us to calculate the quantum tunneling from the black hole to the white hole, and determine the temperature and entropy of the white hole.

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.

A single tree topology is a commonly employed topology for wireless sensor networks (WSN) to connect sensors to one or more remote gateways. However, its many-to-one traffic routing pattern imposes heavy burden on downstream nodes, as the same routes are repeatedly used for packet transfer, from one or more upstream branches. The challenge is how to choose the most optimal routing paths that minimizes energy consumption across the entire network. This paper proposes a proactive energy awareness-based many-to-one traffic routing scheme to alleviate the above said problem referred to as Energy Balance-Based Energy Hole Alleviation in tree topology (EBEHA-T). This protocol combines updated status of variations in energy consumption pattern around sink-hole zones and distribution of joint nodes among the trees. With this approach, EBEHA-T proactively prevents sink-hole formation instead of just a reactive response after they have occurred. Performance evaluation of EBEHA-T against benchmark method RaSMaLai shows increased energy saving across the entire network and a marked improvement in energy consumption balance in energy-hole zones. This precludes energy hole formation and the consequent network partitioning, leading to improved network lifetime beyond that of the RasMaLai. OMNET++ network simulation software has been used for the evaluation.

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.

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.

New modied Hayward metric of magnetically charged non-singular black hole spacetime in the framework of nonlinear electrodynamics is constructed. When the fundamental length introduced, characterising quantum gravity effects, vanishes one comes to the general relativity coupled with the Bronnikov model of nonlinear electrodynamics. The metric can have one (an extreme) horizon, two horizons of black holes, or no horizons corresponding to the particle-like solution. Corrections to the Reissner-Nordström solution are found as the radius approaches to innity. As r -> 0 the metric has a de Sitter core showing the absence of singularities. The asymptotic of the Ricci and Kretschmann scalars are obtained and they are nite everywhere. The thermodynamics of black holes, by calculating the Hawking temperature and the heat capacity, is studied. It is demonstrated that phase transitions take place when the Hawking temperature possesses the maximum. Black holes are thermodynamically stable at some range of parameters.

In this paper only one basic assumption has been made: if we try to describe black holes, their behavior should be understood in the same language as the one we use for particles; black holes should be treated just like atoms. They must be quantum forms of matter, moving in accordance with Schrödinger equations just like everything else. In particular, Rosen’s quantization approach to the gravitational collapse is applied in the simple case of a pressureless “star of dust” by finding the gravitational potential, the Schrödinger equation and the solution for the collapse’s energy levels. By applying the constraints for a Schwarzschild black hole (BH) and by using the concept of BH effective state, previously introduced by one of the authors (CC), the BH quantum gravitational potential, Schrödinger equation and the BH energy spectrum are found. Remarkably, such an energy spectrum is in agreement (in its absolute value) with the one which was conjectured by Bekenstein in 1974 and consistent with other ones in the literature. This approach also permits to find an interesting quantum representation of the Schwarzschild BH ground state at the Planck scale. Moreover, two fundamental issues about black hole quantum physics are addressed by this model: the area quantization and the singularity resolution. As regards the former, a result similar to the one obtained by Bekenstein, but with a different coefficient, has been found. About the latter, it is shown that the traditional classical singularity in the core of the Schwarzschild BH is replaced, in a full quantum treatment, by a two-particle system where the two components strongly interact with each other via a quantum gravitational potential. The two-particle system seems to be non-singular from the quantum point of view and is analogous to the hydrogen atom because it consists of a “nucleus” and an “electron”.

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.

In this paper, we study the weak gravitational deflection angle of relativistic massive particles by the Kerr-like black hole in the bumblebee gravity model. In particular, we focus on weak field limits and calculate the deflection angle for a receiver and source at a finite distance from the lens. To this end, we use the Gauss-Bonnet theorem of a two-dimensional surface defined by a generalized Jacobi metric. The spacetime is asymptotically non-flat due to the existence of a bumblebee vector field. Thus the deflection angle is modified and can be divided into three parts: the surface integral of the Gaussian curvature, the path integral of a geodesic curvature of the particle ray and the change in the coordinate angle. In addition, we also obtain the same results by defining the deflection angle. The effects of the Lorentz breaking constant on the gravitational lensing are analyzed. We then consider the finite-distance correction for the deflection angle of massive particles.

In our recently proposed theory of quantum gravity, a black hole arises from the spontaneous localisation of an entangled state of a large number of atoms of space-time-matter [STM]. Prior to localisation, the non-commutative curvature of an STM atom is described by the spectral action of non-commutative geometry. By using the techniques of statistical thermodynamics from trace dynamics, we show that the gravitational entropy of a Schwarzschild black hole results from the microstates of the entangled STM atoms and is given (subject to certain assumptions) by the classical Euclidean gravitational action. This action, in turn, equals the Bekenstein-Hawking entropy (Area/$4{L_P}^2$) of the black hole. We argue that spontaneous localisation is related to black-hole evaporation through the fluctuation-dissipation theorem.

We use a random gap model to describe a metal-insulator transition in three-dimensional semiconductors due to doping and find a conventional phase transition, where the effective scattering rate is the order parameter. Spontaneous symmetry breaking results in metallic behavior, whereas the insulating regime is characterized by the absence of spontaneous symmetry breaking. The transition is continuous for the average conductivity with critical exponent equal to 1. Away from the critical point the exponent is roughly 0.6, which may explain experimental observations of a crossover of the exponent from 1 to 0.5 by going away from the critical point.

A thin-shell wormhole is crafted by the cut-and-paste method of two Bardeen de-Sitter black holes using Darmois-Israel formalism. Energy conditions are considered for different values of magnetic charge while both mass and cosmological constant are fixed. The attractive and repulsive characteristics of the throat of the thin-shell wormhole are also examined through the radial acceleration. Dynamics and stability of the wormhole are studied around the static solutions of the linearized radial perturbations at the throat of the wormhole. The regions of stability are determined by checking out the condition of concavity of the potential as a function in the throat radius for different values of magnetic charges.

We study the light rays in a static and spherically symmetric gravitational field of null aether theory (NAT). To this end, we employ the Gauss-Bonnet theorem to compute the deflection angle by a NAT black hole in the weak limit approximation. Using the optical metrics of the NAT black hole, we first obtain the Gaussian curvature and then calculate the leading terms of the deflection angle. Our calculations show how gravitational lensing is affected by the NAT field. We also show once again that the bending of light stems from a global and topological effect.

Black hole collision produce gravitational radiation which is generally thought in a quantum limit to be gravitons. The stretched horizon of a black hole contains quantum information, or a form of quantum hair, which in a coalescence of black holes participates in the generation of gravitons. This may be facilitated with a Bohr-like approach to black hole (BH) quantum physics with quasi-normal mode (QNM) approach to BH quantum mechanics. Quantum gravity and quantum hair on event horizons is excited to higher energy in BH coalescence. The near horizon condition for two BHs right before collision is a deformed AdS spacetime. These excited states of BH quantum hair then relax with the production of gravitons. This is then argued to define RT entropy given by quantum hair on the horizons. These qubits of information from a BH coalescence should then appear in gravitational wave (GW) data. This is a form of the standard AdS/CF T correspondence and the Ryu-Takayanagi (RT) formula [1]. The foundations of physics is proposed to be quantum information and a duality between spacetime observables and quantum fields.

The effect of divergence of chute sidewalls with three different baffle block geometries namely USBR, trihedral and semicircular blocks, as well as the depth and dimensions of the scour hole downstream of the chute were studied using a physical model. For this purpose, 9 models of baffled chutes were designed and constructed with divergence ratios of 1.45, 1.75, and 2.45 and without divergence (with a divergence ratio of 1). Comparing the results on the effect of block geometry at different divergence ratios revealed that the use of blocks proposed in this study instead of standard USBR blocks reduced the mean and maximum scour hole by 50%. For a given block geometry, the mean depth, maximum depth, and length of scour hole were reduced by 75%, 58%, and 50%, respectively.

This paper is devoted to investigate charged vector particles tunneling via horizons of a pair of accelerating rotating charged NUT black hole under the influence of quantum gravitational effects. For this purpose, we use the modified Proca equation incorporating generalized uncertainty principle. Using the WKB approximation to the field equation, we obtain a modified tunneling rate and the corresponding corrected Hawking temperature for this black hole. Moreover, we analyze the graphical behavior of corrected Hawking temperature T'_H with respect to the event horizon for the given black hole. By considering quantum gravitational effects on Hawking temperatures, we discuss the stability analysis of this black hole. For a pair of black holes, the temperature T'_H increases with the increase in rotation parameters α and w, correction parameter β, black hole acceleration α and arbitrary parameter k and decreases with the increase in electric e and magnetic charges g.

The calculation of the release of liquid hazardous chemicals storage tanks is an important part of the quantitative risk assessment of accidents. This paper mainly establishes a continuous real–time release model based on the instantaneous mass flow Q_m model. Meanwhile, the software function module was analyzed, and programming software was developed using C# language for model solving. A series of experiments for repeated leakage tests was designed and the discharges through three small holes with different heights for 200 s were observed. The results show that the continuous real–time leakage model is effective, and the deviation between theoretical and experimental release amounts are within a reasonable range. The higher the liquid level above the leak hole is, and the smaller the height of the leak hole from the ground is, the greater the flow rate at the leak orifice is and the smaller discharge rate change is. Therefore, the deviation between the theoretical release amount M_t and the experimental average release amount Ma is greater while the height of the leak hole from the ground is smaller, which indicates that the smaller the distance from the leak orifice to the ground, the greater the influence of the empirical discharge coefficient C₀ on the release amount M.

In this paper, we analyze the Hawking radiation phenomenon for types of Banados-Teitelboim-Zanelli-like (BTZ-like) black holes. For this purpose, using the Hamilton-Jacobi method, we consider semi-classical WKB approximation to calculate the tunneling probabilities of massive boson particles. For these particles, we use the equation of motion for the Glashow-Weinberg-Salam model. Using quantum tunneling process of charged massive bossons, we compute the corresponding Hawking temperatures. Furthermore, we discuss the effects of rotation parameter on tunneling probability and temperature.

A dark region and a bright part of accretion disk are viewed on the first image of the supermassive black hole in the galaxy M87 obtained by the Event Horizon Telescope. We demonstrate that a viewed dark region is a silhouette of the black hole event horizon, while the outline (contour) of this silhouette is an equator of the event horizon globe. A dark silhouette of the black hole event horizon is placed within the expected position of the black hole shadow, which is not revealed on the first image. We calculate numerically a relation between the viewed position of the black hole silhouette and the brightest point in a thin accretion disk in dependence of the black hole spin. A spin of the supermassive black hole in the galaxy M87, derived from this relation, is $a=0.75\pm0.15$.

In this work, we study the weak gravitational lensing in the background of Kerr-Newman black hole with quintessential dark energy. Initially, we compute the deflection angle of light by charged black hole with quintessential dark energy by utilizing the Gauss-Bonnet theorem. Firstly, we suppose the light rays on the equatorial plane in the axisymmetric spacetime. In doing so, we first find the corresponding optical metrics and then calculate the Gaussian optical curvature to utilize in Gauss-Bonnet theorem. Consequently, we calculate the deflection angle of light for rotating charged black hole with quintessence. Additionally, we also find the deflection angle of light for Kerr-Newman black hole with quintessential dark energy. In order to verify our results, we derive deflection angle by using null geodesic equations which reduces to the deflection angle of Kerr solution with the reduction of specific parameters. Furthermore, we analyze the graphical behavior of deflection angle $\Theta$ w.r.t to quintessence parameter $\alpha$, impact parameter $b$, BH charge $Q$ and rotation parameter $a$. Our graphical analysis retrieve various results regarding to the deflection angle by the Kerr-Newman black hole with quintessential dark energy.

In this paper, we are interested in a model of exact asymptotically flat charged hairy black holes in the background of dilaton potential. We study the weak gravitational lensing in the spacetime of hairy black hole in Einstein-Maxwell theory with a non-minimally coupled dilaton and its non-trivial potential. In doing so, we use the optical geometry of the flat charged hairy black hole for some range of parameter $\gamma$. For this purpose, by using Gauss-Bonnet theorem, we obtain the deflection angle of photon in a spherically symmetric and asymptotically flat spacetime. Moreover, we also investigate the impact of plasma medium on weak gravitational lensing by asymptotically flat charged hairy black hole with a dilaton potential. Our analytically analyses show the effect of the hair on the deflection angle in weak field limits.

In this paper, we argue that one can calculate the weak deflection angle in the background of Einstein-Maxwell-Dilaton-Axion black hole using the Gauss-Bonnet theorem. To support this, the optical geometry of the black hole with the Gibbons-Werner method are used to obtain the deflection angle of light in the weak field limits. Moreover, we investigate the effect of a plasma medium on deflection of light for a given black hole. Because of dilaton and axion are one of the candidate of the dark matter, it can give us a hint on observation of dark matter which is supported the black hole. Hence we demonstrate the observational viability via showing the effect of the dark matter on the weak deflection angle.

In this paper, we proposed a new model of non-linear electrodynamics with parameter. Firstly, we study the weak limit approximation and by using the Gauss Bonnet theorem, we obtain the deflection angle of photon from magnetized black hole and effect of bnon-linear electrodynamics. In doing so, we find the corresponding optical metric after that we calculate the Gaussian curvature which is used in Gauss Bonnet theorem. Then we show the deflection angle in the leading order terms. We also analyzed that our results reduces into Maxwell's electrodynamics and RN solution with the reduction of parameters. Moreover, we also investigate the graphical behavior of deflection angle w.r.t correction parameter, black hole charge and impact parameter.

The Universe, rather than being homogeneous, displays an almost infinite topological genus, because it is punctured with a countless number of gravitational vortexes, i.e., black holes. Starting from this view, we aim to show that the occurrence of black holes is constrained by geometric random walks taking place during cosmic inflationary expansion. At first, we introduce a visual model, based on the Pascal’s triangle and linear and nonlinear arithmetic octahedrons, which describes three-dimensional cosmic random walks. In case of nonlinear 3D paths, trajectories in an expanding Universe can be depicted as the operation of filling the numbers of the octahedrons in the form of “islands of numbers”: this leads to separate cosmic structures (standing for matter/energy), spaced out by empty areas (constituted by black holes and dark matter). These procedures allow us to describe the topology of an universe of infinite genus, to assess black hole formation in terms of infinite Betti numbers, to highlight how non-linear random walks might provoke gravitational effects also in absence of mass/energy, and to propose a novel interpretation of Beckenstein-Hawking entropy: it is proportional to the surface, rather than the volume, of a black hole, because the latter does not contain information.

Maxwell's fish eye has been known to be a perfect lens in optics. In this letter, using the Gibbons-Werner method, namely Gauss-Bonnet theorem on optical geometry of black hole, we extend the calculation of the weak gravitational lensing within the Maxwell's fisheye as a perfect lensing in medium composed of an isotropic refractive index that near-field information can be obtained from far-field distances. Moreover, these results provide an excellent tool to observe compact massive object by weak gravitational lensing within the dark matter medium and to understand the nature of the dark matter that may effect the gravitational waves. Moreover, we show that Gauss-Bonnet theorem is a global effect and this method can be used as a new tool on any optical geometry of compact objects in dark matter medium.

We propose a notion of $(q,\sigma,\tau)$-differential graded algebra, which generalizes the notions of $(\sigma,\tau)$-differential graded algebra and $q$-differential graded algebra. We construct two examples of $(q,\sigma,\tau)$-differential graded algebra, where the first one is constructed by means of generalized Clifford algebra with two generators (reduced quantum plane), where we use a $(\sigma,\tau)$-twisted graded $q$-commutator. In order to construct the second example, we introduce a notion of $(\sigma,\tau)$-pre-cosimplicial algebra.

Theoretical approaches to calculate pKa values for Brønsted acids is a challenging task that, most of the time, involves sophisticated and time-consuming methods. Therefore, heuristic approaches are efficient and appealing methodologies to approximate these values. Herein, by considering the electrostatic potential on acidic hydrogen atoms in a similar fashion that a σ–hole is defined, we calculated the maximum surface potential, V_S,max, and used it as a descriptor to correlate it with experimental acidity constants. These values were calculated using the CPCM implicit solvent model (water) with six different methods: five density functionals and the Møller–Plesset second order perturbation theory. Six different basis sets were combined with each method in order to benchmark a total of thirty-six levels of theory. Overall, 1080 calculations were performed and found to correlate with experimental data. The ωB97X-D/6-31+G(d,p) level of theory stands as the best one for consistently reproduce the reported pKa values.

A black hole in a Schwarzschild spacetime is considered. A transformation is proposed that describes the relationship between the coordinate systems exterior and interior to an event horizon. Application of this transformation permits considerations of the (a)symmetry of a range of phenomena taking place on both sides of the event horizon. The paper investigates two distinct problems of a uniformly accelerated particle. In one of these, although the equations of motion are the same in the regions on both sides, the solutions turn out to be very different. This manifests the differences of the properties of these two ranges.

MP2/aug-cc-pVTZ calculations were carried out for the ZFH₃-B complexes (Z = C, Si, Ge, Sn and Pb; B = C₂H₂, C₂H₄, C₆H₆ and C₅H₅^-; relativistic effects were taken into account for Ge, Sn and Pb elements). These calculations are supported by other approaches; the decomposition of the energy of interaction, Quantum Theory of Atoms in Molecules (QTAIM) and Natural Bond Orbital (NBO) method. The results show that tetrel bonds with π-electrons as Lewis bases are classified as Z…C links between single centers (C is an atom of the π-electron system) or as Z…π interactions where F-Z bond is directed to the mid-point (or nearly so) of the CC bond of the Lewis base. The analogues systems with Z…C/π interactions were found in the Cambridge Structural Database (CSD). It was found that the strength of interaction increases with the increase of the atomic number of the tetrel element and that for heavier tetrel elements the ZFH₃ tetrahedral structure is more deformed towards the structure with the planar ZH₃ fragment. The results of calculations show that the tetrel bond is sometimes accompanied by the Z-H…C hydrogen bond or even sometimes the ZFH₃-B complexes are linked only by the hydrogen bond interaction.

Band-gap alignment engineering has now been extensively studied due to its high potential application. Here we demonstrate a simple route to synthesize two metal oxide layers and align them together according to their bandgaps on surface of crystalline silicon (c-Si) solar cells. The metal oxide layers can not only extend absorption spectrum to generate extra carriers but also serve to separate electron-hole pairs more efficiently. As a consequence, the photovoltaic performance of SnO₂/CdO /Si double-layer solar cell (DLSC) is highly improved compared to CdO/Si and SnO₂/Si single-layer solar cells(SLSCs) and SnO₂/CdO/Si double-layer solar cell (DLSC). By the alignment engineering, the SnO₂/CdO/Si DLSC produces a short circuit photocurrent (J_sc) of 38.20 mA/cm², an open circuit photovoltage (V_oc) of 0.575 V and a fill factor (FF) of 68.7%, corresponding to a light to electric power conversion efficiency (η) of 15.09% under AM1.5 illumination. These results suggest that with the use of metal oxide layers by band-gap alignment engineering, new avenues have been opened for developing high-efficiency and cost-effective c-Si solar cells.

In this work it is acknowledged that important attempts to devise an emergent quantum (gravity) theory require space-time to be discretized at the Planck scale. It is therefore conjectured that reality is identical to a sub-quantum dynamics of ontological micro-constituents that are connected by a single interaction law. To arrive at a complex system-based toy-model identification of these micro-constituents, two strategies are combined. First, by seeing gravity as an entropic phenomenon and generalizing the dimensional reduction of the associated holographic principle, the universal constants of free space are related to assumed attributes of the micro-constituents. Second, as the effective field dynamics of the micro-constituents must eventually obey Einstein’s field equations, a sub-quantum interaction law is derived from a solution of these equations. A Planck-scale origin for thermodynamic black hole characteristics and novel views on entropic gravity theory result from this approach, which eventually provides a different view on quantum gravity and its unification with the fundamental forces.

In this work, we present some results related with the issue of the Loop Quantum Black Holes (LQBH) thermodynamics by the use of the tunneling radiation formalism. The information loss paradox is also discussed in this context, where we have considered the influence of back reaction effects.