The Gravitational Energy Problem for Cosmological Models in Teleparallel Gravity

TL;DR

This paper introduces a new method to compute gravitational energy in cosmological models within teleparallel gravity, especially when boundary conditions are not specified, and applies it to key solutions like Schwarzschild-de Sitter and Robertson-Walker universes.

Contribution

The paper develops a boundary-condition-independent approach to gravitational energy in teleparallel gravity and demonstrates its application to important cosmological solutions.

Findings

Average energy density for Schwarzschild-de Sitter spacetime

Energy vanishes for null curvature Robertson-Walker universe

Method applicable without asymptotic boundary conditions

Abstract

We present a method to calculate the gravitational energy when asymptotic boundary conditions for the space-time are not given. This is the situation for most of the cosmological models. The expression for the gravitational energy is obtained in the context of the teleparallel equivalent of general relativity. We apply our method first to the Schwarzschild-de Sitter solution of Einstein's equation, and then to the Robertson-Walker Universe. We show that in the first case our method leads to an average energy density of the vacuum space-time, and in latter case the energy vanishes in the case of null curvature.