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.

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.

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.

scholarly journals String theory at order α′2 and the generalized Bergshoeff-de Roo identification

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Stanislav Hronek ◽  
Linus Wulff
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Strong Evidence ◽  
Degrees Of Freedom ◽  
Heterotic String ◽  
Lorentz Transformations ◽  
Covariant Formalism ◽  
Double Field Theory ◽  
Two Parameter ◽  
Parameter Deformation

Abstract It has been shown by Marques and Nunez that the first α′-correction to the bosonic and heterotic string can be captured in the O(D, D) covariant formalism of Double Field Theory via a certain two-parameter deformation of the double Lorentz transformations. This deformation in turn leads to an infinite tower of α′-corrections and it has been suggested that they can be captured by a generalization of the Bergshoeff-de Roo identification between Lorentz and gauge degrees of freedom in an extended DFT formalism. Here we provide strong evidence that this indeed gives the correct α′2-corrections to the bosonic and heterotic string by showing that it leads to a cubic Riemann term for the former but not for the latter, in agreement with the known structure of these corrections including the coefficient of Riemann cubed.

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.

Conserved quantities of spinning test particles in general relativity. I

1981 ◽  
Vol 375 (1761) ◽  
pp. 185-193 ◽  
Keyword(s):  
General Relativity ◽  
Vector Field ◽  
Tensor Field ◽  
General Scheme ◽  
Killing Vector ◽  
Conserved Quantity ◽  
General Linear ◽  
Killing Vector Field ◽  
Conserved Quantities ◽  
Test Particles

This is the first of two papers devoted to conserved quantities of spinning test particles in general relativity. In this paper, a general scheme is described according to which these quantities can be investigated. It is shown that the general linear conserved quantity consists of a sum, the first term of which is the well known expression constructed from a Killing vector field, and the second term is of the form U kl S kl , where U* ab is a Killing-Yano tensor field, which is constrained by two additional equations.

scholarly journals THE RELATIVE ENERGY OF HOMOGENEOUS AND ISOTROPIC UNIVERSES FROM VARIATIONAL PRINCIPLES

2009 ◽  
Vol 06 (07) ◽  
pp. 1193-1205 ◽  
Author(s):  
ENRICO BIBBONA ◽  
LORENZO FATIBENE ◽  
MAURO FRANCAVIGLIA
Keyword(s):  
Vector Fields ◽  
Variational Principles ◽  
Cosmic Time ◽  
Matching Condition ◽  
Relative Energy ◽  
Conserved Quantity ◽  
Conserved Quantities ◽  
Time Coordinate ◽  
Poincaré Algebra ◽  
Conserved Currents

We calculate the relative conserved currents, superpotentials and conserved quantities between two homogeneous and isotropic universes. In particular, we prove that their relative "energy" (defined as the conserved quantity associated to cosmic time coordinate translations for a comoving observer) is vanishing and so are the other conserved quantities related to a Lie subalgebra of vector fields isomorphic to the Poincaré algebra. These quantities are also conserved in time. We also find a relative conserved quantity for such a kind of solution which is conserved in time though non-vanishing. This example provides at least two insights in the theory of conserved quantities in General Relativity. First, the contribution of the cosmological matter fluid to the conserved quantities is carefully studied and proved to be vanishing. Second, we explicitly show that our superpotential (that happens to coincide with the so-called KBL potential although it is generated differently) provides strong conservation laws under much weaker hypotheses than the ones usually required. In particular, the symmetry generator is not needed to be Killing (nor Killing of the background, nor asymptotically Killing), the prescription is quasi-local and it works fine in a finite region too and no matching condition on the boundary is required.

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 f-SYMBOLS, KILLING TENSORS AND CONSERVED BEL-TYPE CURRENTS

2011 ◽  
Vol 26 (05) ◽  
pp. 337-349
Author(s):  
OVIDIU TINTAREANU-MIRCEA
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Killing Vector Fields ◽  
Killing Tensors ◽  
Einstein Spaces ◽  
Conserved Currents

In the framework of the General Relativity we show that from three generalizations of Killing vector fields, namely f-symbols, symmetric Stäckel–Killing and antisymmetric Killing–Yano tensors, some conserved currents can be obtained through adequate contractions of the above-mentioned objects with rank-four tensors having the properties of Bel or Bel–Robinson tensors in Einstein spaces.

scholarly journals (SUPER)n-ENERGY FOR ARBITRARY FIELDS AND ITS INTERCHANGE: CONSERVED QUANTITIES

2000 ◽  
Vol 15 (03) ◽  
pp. 159-165 ◽  
Author(s):  
JOSÉ M. M. SENOVILLA
Keyword(s):  
Scalar Field ◽  
Killing Vector ◽  
Conserved Quantities ◽  
Algebraic Construction ◽  
Classical Work ◽  
Propagation Law ◽  
Maxwell Fields ◽  
Dominant Property ◽  
Physical Fields ◽  
Mathematical Characteristics

Inspired by classical work of Bel and Robinson, a natural purely algebraic construction of super-energy (s-e) tensors for arbitrary fields is presented, having good mathematical and physical properties. Remarkably, there appear quantities with mathematical characteristics of energy densities satisfying the dominant property, which provides s-e estimates useful for global results and helpful in other matters. For physical fields, higher order (super)n-energy tensors involving the field and its derivatives arise. In special relativity, they provide infinitely many conserved quantities. The interchange of s-e between different fields is shown. The discontinuity propagation law in Einstein–Maxwell fields is related to s-e tensors, providing quantities conserved along null hypersurfaces. Finally, conserved s-e currents are found for any minimally coupled scalar field whenever there is a Killing vector.

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