scholarly journals An Alternative Approach to the Static Spherically Symmetric, Vacuum Global Solution to the Einstein Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Luis Herrera ◽  
Louis Witten
Keyword(s):  
Phase Transition ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
Angle Variable ◽  
Schwarzschild Black Hole ◽  
Alternative Description ◽  
Complex Transformation ◽  
Test Particles ◽  
Alternative Approach ◽  
Symmetric Vacuum

We propose an alternative description of the Schwarzschild black hole based on the requirement that the solution is static not only outside the horizon but also inside it. As a consequence of this assumption, we are led to a change of signature implying a complex transformation of an angle variable. There is a “phase transition” on the surface R=2m, producing a change in the symmetry as we cross this surface. Some consequences of this situation on the motion of test particles are investigated.

scholarly journals Classical Polymerization of the Schwarzschild Metric

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Babak Vakili
Keyword(s):  
Energy Momentum Tensor ◽  
Vacuum Solution ◽  
Equations Of Motion ◽  
Hamiltonian Function ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric ◽  
Similarities And Differences

We study a spherically symmetric setup consisting of a Schwarzschild metric as the background geometry in the framework of classical polymerization. This process is an extension of the polymeric representation of quantum mechanics in such a way that a transformation maps classical variables to their polymeric counterpart. We show that the usual Schwarzschild metric can be extracted from a Hamiltonian function which in turn gets modifications due to the classical polymerization. Then, the polymer corrected Schwarzschild metric may be obtained by solving the polymer-Hamiltonian equations of motion. It is shown that while the conventional Schwarzschild space-time is a vacuum solution of the Einstein equations, its polymer-corrected version corresponds to an energy-momentum tensor that exhibits the features of dark energy. We also use the resulting metric to investigate some thermodynamical quantities associated with the Schwarzschild black hole, and in comparison with the standard Schwarzschild metric the similarities and differences are discussed.

scholarly journals Spherically symmetric vacuum solutions arising from trace dynamics modifications to gravitation

2015 ◽  
Vol 24 (02) ◽  
pp. 1550011 ◽  
Author(s):  
Stephen L. Adler ◽  
Fethi M. Ramazanoğlu
Keyword(s):  
Einstein Equations ◽  
Polar Coordinates ◽  
Spherically Symmetric ◽  
Static Case ◽  
Isotropic Coordinates ◽  
Physical Singularity ◽  
Symmetric Vacuum ◽  
Polar Radius ◽  
Vacuum Solutions ◽  
Time Dependent Solution

We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action (derived from trace dynamics) that gives an alternative explanation of the origin of "dark energy". We give analytic and numerical results for the solutions of these equations, first in polar coordinates, and then in isotropic coordinates. General features of the static case are that: (i) there is no horizon, since g00 is nonvanishing for finite values of the polar radius, and only vanishes (in isotropic coordinates) at the internal singularity, (ii) the Ricci scalar R vanishes identically, and (iii) there is a physical singularity at cosmological distances. The large distance singularity may be an artifact of the static restriction, since we find that the behavior at large distances is altered in a time-dependent solution using the McVittie Ansatz.

scholarly journals SOME REMARKS ON THE EINSTEIN AND MØLLER PSEUDOTENSORS FOR STATIC AND SPHERICALLY-SYMMETRIC CONFIGURATIONS

2008 ◽  
Vol 23 (08) ◽  
pp. 591-601 ◽  
Author(s):  
JERZY MATYJASEK
Keyword(s):  
Black Hole ◽  
Spherically Symmetric ◽  
Schwarzschild Black Hole ◽  
Static Systems

It is shown that for the spherically-symmetric and static systems the hypotheses posed by Yang and Radinschi and by Vagenas can be related to the particular distribution of the source. Simple proofs are given and a number of examples are discussed with the special emphasis put on the quantum corrected Schwarzschild black hole.

scholarly journals Deformed General Relativity and Quantum Black Holes Interior

Universe ◽  
2020 ◽  
Vol 6 (3) ◽  
pp. 39 ◽  
Author(s):  
Denis Arruga ◽  
Jibril Ben Achour ◽  
Karim Noui
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Einstein Equations ◽  
Gravity Models ◽  
Effective Theory ◽  
Hamiltonian Constraint ◽  
Spherically Symmetric ◽  
Full Generality ◽  
Full Theory ◽  
Effective Theories

Effective models of black holes interior have led to several proposals for regular black holes. In the so-called polymer models, based on effective deformations of the phase space of spherically symmetric general relativity in vacuum, one considers a deformed Hamiltonian constraint while keeping a non-deformed vectorial constraint, leading under some conditions to a notion of deformed covariance. In this article, we revisit and study further the question of covariance in these deformed gravity models. In particular, we propose a Lagrangian formulation for these deformed gravity models where polymer-like deformations are introduced at the level of the full theory prior to the symmetry reduction and prior to the Legendre transformation. This enables us to test whether the concept of deformed covariance found in spherically symmetric vacuum gravity can be extended to the full theory, and we show that, in the large class of models we are considering, the deformed covariance cannot be realized beyond spherical symmetry in the sense that the only deformed theory which leads to a closed constraints algebra is general relativity. Hence, we focus on the spherically symmetric sector, where there exist non-trivial deformed but closed constraints algebras. We investigate the possibility to deform the vectorial constraint as well and we prove that non-trivial deformations of the vectorial constraint with the condition that the constraints algebra remains closed do not exist. Then, we compute the most general deformed Hamiltonian constraint which admits a closed constraints algebra and thus leads to a well-defined effective theory associated with a notion of deformed covariance. Finally, we study static solutions of these effective theories and, remarkably, we solve explicitly and in full generality the corresponding modified Einstein equations, even for the effective theories which do not satisfy the closeness condition. In particular, we give the expressions of the components of the effective metric (for spherically symmetric black holes interior) in terms of the functions that govern the deformations of the theory.

scholarly journals Shapovalov Wave-Like Spacetimes

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1372 ◽  
Author(s):  
Konstantin Osetrin ◽  
Evgeny Osetrin
Keyword(s):  
Jacobi Equation ◽  
Eikonal Equation ◽  
Separation Of Variables ◽  
Complete Classification ◽  
Complete Separation ◽  
Einstein Equations ◽  
Coordinate Systems ◽  
Test Particles ◽  
Hamilton Jacobi Equation

A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton–Jacobi equation for a test particle is integrated by the method of complete separation of variables with separation of the isotropic (wave) variable, on which the metric depends (wave-like Shapovalov spaces). For all types of Shapovalov spaces, exact solutions of the Einstein equations with a cosmological constant in vacuum are found. Complete integrals are presented for the eikonal equation and the Hamilton–Jacobi equation of motion of test particles.

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