A moving black hole in TEGR as a moving matter ball

TL;DR

This paper explores a covariant formalism in TEGR to analyze a moving Schwarzschild black hole, constructing invariant mass and momentum, and drawing an analogy to a moving matter ball in Minkowski space.

Contribution

It applies a covariant TEGR formalism to a moving black hole solution, achieving invariant conserved quantities without relying on Killing vectors.

Findings

Successfully constructs invariant mass and momentum for the moving black hole.

Demonstrates the formalism's effectiveness in non-Killing vector scenarios.

Establishes an analogy between black hole and matter ball dynamics.

Abstract

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.