scholarly journals On conserved quantities for the Schwarzschild black hole in teleparallel gravity

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
E. D. Emtsova ◽  
M. Krššák ◽  
A. N. Petrov ◽  
A. V. Toporensky
Keyword(s):  
Black Hole ◽  
Initial Velocity ◽  
Killing Vector ◽  
Teleparallel Gravity ◽  
Spin Connection ◽  
Conserved Quantities ◽  
Covariant Formulation ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Solution ◽  
Gravity Method

AbstractWe examine various methods of constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR). We demonstrate that in the covariant formulation the preferred method are the Noether charges that are true invariant quantities. The Noether charges depend on the vector field $$\xi $$ ξ and we consider two different options where $$\xi $$ ξ is chosen as either a Killing vector or a four-velocity of the observer. We discuss the physical meaning of each choice on the example of the Schwarzschild solution in different frames: static, freely falling Lemaitre frame, and a newly obtained generalised freely falling frame with an arbitrary initial velocity. We also demonstrate how to determine an inertial spin connection for various tetrads used in our calculations, and find a certain ambiguity in the “switching-off” gravity method where different tetrads can share the same inertial spin connection.

scholarly journals On the Schwarzschild solution in TEGR

2021 ◽  
Vol 2081 (1) ◽  
pp. 012017
Author(s):  
E D Emtsova ◽  
M Krššák ◽  
A N Petrov ◽  
A V Toporensky
Keyword(s):  
Initial Velocity ◽  
Killing Vector ◽  
Spin Connection ◽  
Lorentz Transformations ◽  
Conserved Quantities ◽  
Schwarzschild Black Hole ◽  
Covariant Formalism ◽  
Schwarzschild Solution ◽  
Free Falling ◽  
Conserved Currents

Abstract Conserved currents, superpotentials and charges for the Schwarzschild black hole in the Teleparallel Equivalent of General Relativity (TEGR) are constructed. We work in the covariant formalism and use the Noether machinery to construct conserved quantities that are covariant/invariant with respect to both coordinate and local Lorentz transformations. The constructed quantities depend on the vector field ξ and we consider two different possibilities, when ξ is chosen as either a timelike Killing vector or a four-velocity of an observer. We analyze and discuss the physical meaning of each choice in different frames: static and freely falling Lemaitre frame. Moreover, a new generalized free-falling frame with an arbitrary initial velocity at infinity is introduced. We derive the inertial spin connection for various tetrads in different frames and find that the “switching-off” gravity method leads to ambiguities.

DE SITTER-SCHWARZSCHILD BLACK HOLE: ITS PARTICLELIKE CORE AND THERMODYNAMICAL PROPERTIES

1996 ◽  
Vol 05 (05) ◽  
pp. 529-540 ◽  
Author(s):  
I.G. DYMNIKOVA
Keyword(s):  
Black Hole ◽  
Lower Limit ◽  
Mass Parameter ◽  
Hawking Temperature ◽  
Einstein Equations ◽  
Black Hole Mass ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Solution ◽  
Second Order Phase Transition

We analyze the globally regular solution of the Einstein equations describing a black hole whose singularity is replaced by the de Sitter core. The de Sitter—Schwarzschild black hole (SSBH) has two horizons. Inside of it there exists a particlelike structure hidden under the external horizon. The critical value of mass parameter M cr1 exists corresponding to the degenerate horizon. It represents the lower limit for a black-hole mass. Below M cr1 there is no black hole, and the de Sitter-Schwarzschild solution describes a recovered particlelike structure. We calculate the Hawking temperature of SSBH and show that specific heat is broken and changes its sign at the value of mass M cr 2>M cr 1 which means that a second-order phase transition occurs at that point. We show that the Hawking temperature drops to zero when a mass approaches the lower limit M cr1 .

scholarly journals GRAVITATIONAL CAPTURE OF COSMIC STRINGS BY A BLACK HOLE

1998 ◽  
Vol 07 (06) ◽  
pp. 957-967 ◽  
Author(s):  
JEAN-PIERRE DE VILLIERS ◽  
VALERI FROLOV
Keyword(s):  
Black Hole ◽  
Impact Parameter ◽  
Cosmic String ◽  
Initial Velocity ◽  
Cosmic Strings ◽  
Gravitational Interaction ◽  
Equations Of Motion ◽  
Great Distance ◽  
Schwarzschild Black Hole ◽  
Gravitational Capture

The gravitational interaction of an infinitely long cosmic string with a Schwarzschild black hole is studied. We consider a straight string that is initially at a great distance and moving at some initial velocity v (0 < v < c) towards the black hole. The equations of motion of the string are solved numerically to obtain the dependence of the capture impact parameter on the initial velocity.

Physics in Curved Spacetime

2021 ◽  
pp. 211-253
Author(s):  
Moataz H. Emam
Keyword(s):  
Black Hole ◽  
Vector Fields ◽  
Killing Vector ◽  
Schwarzschild Black Hole ◽  
Curved Spacetime ◽  
Killing Vector Fields ◽  
Event Horizons ◽  
Free Particles ◽  
Generally Covariant

We discuss mechanics in curved spacetime backgrounds, gravitational time dilation, the motion of free particles, geodesics. We use the Schwarzschild metric as a case study and solve for motion along radial and orbital geodesics. This includes the strange behaviour around the event horizons of a Schwarzschild black hole. Isometries and Killing vector fields are explained and applied. Finally a brief presentation of generally covariant electrodynamics is given.

scholarly journals On the Gauge Fixing in the Hamiltonian Analysis of General Teleparallel Theories

Universe ◽  
2019 ◽  
Vol 5 (6) ◽  
pp. 143 ◽  
Author(s):  
Daniel Blixt ◽  
Manuel Hohmann ◽  
Christian Pfeifer
Keyword(s):  
Degrees Of Freedom ◽  
Teleparallel Gravity ◽  
Spin Connection ◽  
Lorentz Transformations ◽  
Covariant Formulation ◽  
Gauge Fixing ◽  
Theories Of Gravity ◽  
Gravity Theories ◽  
6 Degrees Of Freedom ◽  
Hamiltonian Analysis

The covariant formulation of teleparallel gravity theories must include the spin connection, which has 6 degrees of freedom. One can, however, always choose a gauge such that the spin connection is put to zero. In principle this gauge may affect counting of degrees of freedom in the Hamiltonian analysis. We show for general teleparallel theories of gravity, that fixing the gauge such that the spin connection vanishes in fact does not affect the counting of degrees of freedom. This manifests in the fact that the momenta of the Lorentz transformations which generate the spin connection are fully determined by the momenta of the tetrads.

scholarly journals Light from Schwarzschild black holes in de Sitter expanding universe

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Ion I. Cotăescu
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Moving Frame ◽  
Conserved Quantities ◽  
Expanding Universe ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Peculiar Velocities ◽  
Algebraic Code ◽  
Maple Code

AbstractA new method is applied for deriving simultaneously the redshift and shadow of a Schwarzschild black hole moving freely in the de Sitter expanding universe as recorded by a remote co-moving observer. This method is mainly algebraic, focusing on the transformation of the conserved quantities under the de Sitter isometry relating the black hole co-moving frame to observer’s one. Hereby one extracts the general expressions of the redshifts and shadows of the black holes having peculiar velocities but their expressions are too extended to be written down here. Therefore, only some particular cases and intuitive expansions are presented while the complete results are given in an algebraic code (Cotăescu in Maple code BH01, https://physics.uvt.ro/~cota/CCFT/codes, 2020).

scholarly journals Kerr–Schild metrics in teleparallel gravity

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Markus B. Fröb
Keyword(s):  
Black Hole ◽  
Equations Of Motion ◽  
Teleparallel Gravity ◽  
Null Vector ◽  
Spin Connection ◽  
Rotating Black Hole ◽  
Flat Background ◽  
The One

AbstractWe show that the Kerr–Schild ansatz can be extended from the metric to the tetrad, and then to teleparallel gravity where curvature vanishes but torsion does not. We derive the equations of motion for the Kerr–Schild null vector, and describe the solution for a rotating black hole in this framework. It is shown that the solution depends on the chosen tetrad in a non-trivial way if the spin connection is fixed to be the one of the flat background spacetime. We show furthermore that any Kerr–Schild solution with a flat background is also a solution of $$f({\mathcal {T}})$$ f ( T ) gravity.

scholarly journals Horizon shells: Classical structure at the horizon of a black hole

2016 ◽  
Vol 25 (12) ◽  
pp. 1644010 ◽  
Author(s):  
Matthias Blau ◽  
Martin O’Loughlin
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Infinite Number ◽  
Mass Formula ◽  
Black Hole Physics ◽  
Einstein Equations ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Solution ◽  
Classical Structure ◽  
Codimension One

We address the question of the uniqueness of the Schwarzschild black hole by considering the following question: How many meaningful solutions of the Einstein equations exist that agree with the Schwarzschild solution (with a fixed mass [Formula: see text]) everywhere except maybe on a codimension one hypersurface? The perhaps surprising answer is that the solution is unique (and uniquely the Schwarzschild solution everywhere in spacetime) unless the hypersurface is the event horizon of the Schwarzschild black hole, in which case there are actually an infinite number of distinct solutions. We explain this result and comment on some of the possible implications for black hole physics.

The Schwarzschild black hole

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Equilibrium Configuration ◽  
Original Form ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric ◽  
Schwarzschild Geometry

This chapter discusses the Schwarzschild black hole. It demonstrates how, by a judicious change of coordinates, it is possible to eliminate the singularity of the Schwarzschild metric and reveal a spacetime that is much larger, like that of a black hole. At the end of its thermonuclear evolution, a star collapses and, if it is sufficiently massive, does not become stabilized in a new equilibrium configuration. The Schwarzschild geometry must therefore represent the gravitational field of such an object up to r = 0. This being said, the Schwarzschild metric in its original form is singular, not only at r = 0 where the curvature diverges, but also at r = 2m, a surface which is crossed by geodesics.

Sign in / Sign up

Export Citation Format

Share Document