ARTICLE | doi:10.20944/preprints202102.0053.v1
Subject: Engineering, Automotive Engineering Keywords: Ricci flow; Ricci solitons; geodesics; seismic waves
Online: 1 February 2021 (15:21:36 CET)
The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov- functions, the first associated with slipping in a finite period of time, and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to the minimization of the displacements of the floors. 3D Ricci solitons projection via a semi-conformal mapping to a surface is also studied.
ARTICLE | doi:10.20944/preprints202107.0646.v3
Subject: Physical Sciences, General & Theoretical Physics Keywords: General relativity; Uncertainty principle; Geodesics; Black hole singularity; vacuum energy; Quantum gravity; Planck star
Online: 25 August 2021 (09:01:26 CEST)
The classical uncertainty principle inequalities were imposed as a mathematical constraint over the general relativity geodesic equation. In this way, the uncertainty principle was reformulated in terms of the proper space-time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirmed the necessity for a minimum length for the space-time line element in the geodesic, dependent on a geodesic-derived scalar which made the expression Lorentz-covariant. In agreement with quantum gravity theories, GeUP required the imposition of a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone was found around the singularity where uncertainty in space-time diverged to infinity.
ARTICLE | doi:10.20944/preprints202108.0390.v1
Subject: Physical Sciences, General & Theoretical Physics Keywords: Gravitation; Black hole; Shadow; High-energy physics; Cross-section; Null geodesics
Online: 18 August 2021 (14:31:11 CEST)
This letter aims to show the connection between the sinc approximation for high-energy absorption cross section and the shadow radius of the spherically symmetric black hole. This connection can give a physical interpretation of the absorption cross section in the eikonal limit parameters. Moreover, the use of this alternative way, one can extract its shadow radius from the absorption cross section in high energy limits to gain more information about the black hole spacetime. Our results indicate that the increasing the value of the shadow radius of the black hole, exponentially increase the the absorption cross section of the black hole in high-energy limits which can be captured by the Event Horizon Telescope (EHT) collaboration.
ARTICLE | doi:10.20944/preprints202205.0257.v2
Subject: Physical Sciences, General & Theoretical Physics Keywords: Relativistic material particles; active gravitational mass; Lorentz transformations; isotropic Schwarzschild metric; geodesics equations
Online: 8 August 2022 (05:27:29 CEST)
A cloud of relativistic material particles is considered, for which the distortions of length and time caused by the presence of the Lorentz factor an order of magnitude greater than curvature of space-time by gravity. The gravitational mass of the cloud is found in the region where its size is insignificant. It is established that the coefficient of dependence of the cloud mass on the total rest mass of its particles includes a complete elliptic integral of the 2nd kind.
REVIEW | doi:10.20944/preprints202208.0347.v1
Subject: Physical Sciences, General & Theoretical Physics Keywords: General relativity; uncertainty principle; geodesics; black hole singularity; quantum gravity; Planck star; Lorentz invariance violations.
Online: 18 August 2022 (11:06:06 CEST)
Quantum gravity theories rely on a minimal measurable length for their formulations, which clashes with the classical formulation of the uncertainty principle and with Lorentz invariance from general relativity. These incompatibilities led to the development of the generalized uncertainty principle (GUP) from string theories and its various modifications. GUP and covariant formulations of the uncertainty principle are discussed, together with implications for space-time quantization.
ARTICLE | doi:10.20944/preprints202104.0293.v1
Subject: Physical Sciences, Acoustics Keywords: Photon Spheres, Jacobi Lines, Turning Points, Photon Trajectories, Geodesics, Path Tracing Curves, Oscillation Points, Half-Librations
Online: 12 April 2021 (12:37:30 CEST)
In case of the maximally rotating Black Holes (BH) through Kerr-Neumann frames, or as described in Boyer-Lindquist coordinates metrics, the rotation axis of the BHs inputs a frame dragging effect i.e., relativistically a Lens-Thirring Precession that accelerates the photon trajectories oscillates with a shaped induced rotations through the ring singularity, between alternate universes, as a means of an induced geodesics that takes a sharp turning points back and forth provided, in the prograde photon sphere, due to magnetorotational instability, the path tracing of a photons circulates as a smooth fiber bundles over the event horizon curves, that when gets interpolate between mixed trajectories behaves as a geodesics and thus forms a smooth Jacobi-fields through Jacobi-lines by mutual intersection of geodesics over the photon sphere which when somehow gets leaked inside the event horizon, then gets sucked in with not sufficient escape velocity for retardation and trapped in the compact singularity, oscillating back and forth through alternate universes.
ARTICLE | doi:10.20944/preprints202112.0142.v1
Subject: Physical Sciences, Mathematical Physics Keywords: General relativity; geodesics; digitization; quantization; Schwarzschild; Kruskal-Szekeres; singularity; Lambert; tachyon; arbitrary precision calculation; complex time; Lorentz boost
Online: 8 December 2021 (14:49:36 CET)
The geodesics on a relativistic manifold are given by the well-known equation involving the Christoffel coefficients. This equation can be solved numerically step by step and transposed into a quantization. We study here the effect of this quantization on the Schwarzschild spacetime, more precisely in the Kruskal-Szekeres map.