The Teleparallel Equivalent of General Relativity and the Gravitational Centre of Mass

TL;DR

This paper reviews the teleparallel equivalent of general relativity, focusing on the gravitational centre of mass, and explores its implications for dark energy and dark matter localization in various spacetime models.

Contribution

It introduces a detailed analysis of the gravitational centre of mass density within the teleparallel framework, addressing its role in dark energy and dark matter distribution.

Findings

Expression for gravitational centre of mass density is clarified.

Analysis of dark energy localization in Schwarzschild-de Sitter spacetime.

Investigation of gravitational centre of mass in dark matter and axially symmetric spacetimes.

Abstract

We present a brief review of the teleparallel equivalent of general relativity and analyse the expression for the centre of mass density of the gravitational field. This expression has not been sufficiently discussed in the literature. One motivation for the present analysis is the investigation of the localization of dark energy in the three-dimensional space, induced by a cosmological constant in a simple Schwarzschild-de Sitter space-time. We also investigate the gravitational centre of mass density in a particular model of dark matter, in the space-time of a point massive particle and in an arbitrary space-time with axial symmetry. The results are plausible, and lead to the notion of gravitational centre of mass (COM) distribution function.