arXiv subjects

E. D. Emtsova

Publications and source records attributed to E. D. Emtsova.

7 recordsLinked to original sources

arXiv2026

The field-theoretical formalism for TEGR

The teleparallel equivalent of general relativity (TEGR) is represented in a field-theoretical form, where tetrad and matter perturbations are propagated on a background solution of TEGR. Thus, the background tetrad and metric satisfy the background Einstein field equations. This presentation, where perturbations can be finite (not infinitesimal or approximate), is equivalent to the original form of TEGR. The background can be arbitrary, usually corresponding to the solution of TEGR under consideration. Such a formalism is Lagrangian based, where perturbations are classified as dynamic fields, and varying the Lagrangian with respect to dynamic variables leads to the equations for perturbations. Gauge (inner) transformations are defined, and the gauge invariance of the Lagrangian and the field equations are stated. Applying the Noether theorem to the Lagrangian we construct conserved currents, related superpotentials and charges. As an application, we have considered linear gravitational equations on the Ricci-flat background and analyzed their properties, finally deriving gravitational wave equations and the tetrad perturbations in TT-gauge. By new formulae for charges, we have calculated the mass for the Schwarzschild and Kerr black holes and the angular momentum for the Kerr solution. The results are quite acceptable, which signals that the new formalism is powerful, can be used further, and has a potential for future development that can be applied to generalizations of TEGR.

gr-qc↗

arXiv2025

The Noether formalism for constructing conserved quantities in teleparallel equivalents of general relativity

This paper brings a methodological character where we present a comprehensive formalism for constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General Relativity (STEGR). It was developed in series of our earlier works and, here, we unite it into a complete form. By employing the Noether method within a tensor formalism, conserved currents, superpotentials, and charges are constructed. These are shown to be covariant under coordinate transformations and local Lorentz rotations in TEGR, while in STEGR, they are covariant under coordinate transformations. The teleparallel (flat) connections in both theories are defined using the "turning off gravity" principle. Uniting such defined flat connections with tetrad in TEGR and metric in STEGR a new fruitful in applications notion "gauge" is introduced. The choice of various initial tetrads in TEGR or initial coordinates in STEGR leads to different gauges, what gives different conserved quantities. Finally, we discuss an appropriate choice of gauges from a possible set of them.

gr-qc↗

arXiv2025

Mass and angular momentum for the Kerr black hole in TEGR and STEGR

We study the energy-momentum characteristics of the rotating black hole - Kerr solution of general relativity in the Teleparallel Equivalent of General Relativity (TEGR) and the Symmetric Teleparallel Equivalent of General Relativity (STEGR). The previously constructed spacetime covariant and Lorentz invariant expressions for conserved Noether currents, superpotentials and charges are used. The Noether charges describe total energy, momentum or angular momentum of gravitating system depending on a choice of the displacement vector $ξ$. To define covariant and invariant conserved quantities both in TEGR and in STEGR on needs to use external fields which are flat teleparallel connections. To determine the non-dynamical connections in TEGR and STEGR we use the unified ``turning off'' gravity principle. Besides, to analyse the Noether conserved quantities in these theories, we use the concept of ``gauges''. The gauge changing can affect the Noether conserved quantities. We highlight two ways to turn off gravity - by $M \to 0$ and by $M \to 0 , ~ a \to 0$ which gives us different gauges in TEGR and STEGR. In both kind of gauges we get the expected values of black hole mass and angular momentum. Our attempts to find gauges which could lead to a correspondence to Einstein's equivalence principle for the Kerr solution where unsuccessful both in TEGR and STEGR. However, these exercises helped us to find a related gauge for the Schwarzschild solution in STEGR that is a novelty.

physics.gen-ph↗

arXiv2023

Conserved quantities in STEGR and applications

We derive conservation laws in Symmetric Teleparallel Equivalent of General Relativity (STEGR) with direct application of Noether's theorem. This approach allows us to construct covariant conserved currents, corresponding superpotentials and invariant charges. A necessary component of our constructions is the concept of "turning off" gravity, introduced in the framework of STEGR to define the flat and torsionless connection. By calculating currents, one can obtain local characteristics of gravitational field like energy density. Surface integration of superpotentials gives charges which correspond to global quantities of the system like mass, momentum, etc. To test our results for the obtained currents and superpotentials, we calculate the energy density measured by freely falling observer in the simple solutions (Friedman universe, Schwartzchild black hole) and total mass of the Schwartzchild black hole. We find ambiguities in obtaining the connection, which explicitly affect the values of conserved quantities, and discuss possible solutions to this problem.

gr-qc↗

arXiv2023

A moving black hole in TEGR as a moving matter ball

Possibilities of the covariant with respect to both coordinate and local Lorentz transformations formalism developed earlier in the framework of Teleparallel Equivalent of General Relativity (TEGR) are studied. The formalism is applied to a solution for a moving with constant velocity (with respect to distant static observers) Schwarzschild black hole. Coordinate and Lorentz invariant global conserved mass and momentum are constructed. The acceptable results are obtained in spite of the solution under consideration has no, at least, Killing vectors of space displacements. Calculations are quite analogous to calculating the mass and momentum of a moving matter ball in Minkowski space, and this analogy is used essentially.

gr-qc↗

arXiv2021

On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity

We 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 $ξ$ and we consider two different options where $ξ$ 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 the 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.

gr-qc↗

arXiv2018

Phenomenological Extension for Tidal Charge Black Hole

A simple phenomenological extension of the black hole solution with tidal charge is proposed. Empirical data on the Sgr A* is consistent with the suggested metric which serves as a generalisation of the Reissner-Nordstrom one. Such a generalisation includes the leading effects beyond general relativity so, the discussed metric can explain wider range of gravitational effects. We discuss physical features of an object described by the proposed metric, namely, the size of its shadow and the innermost stable circular orbit radius.

gr-qc↗