Localization of Energy in General Relativity

TL;DR

This paper discusses defining and calculating gravitational energy in the teleparallel equivalent of general relativity, including energy within a Schwarzschild black hole, providing a clear approach to energy localization.

Contribution

It introduces a natural and unambiguous way to define energy density in teleparallel gravity and applies it to compute energy inside black holes.

Findings

Energy density can be naturally defined in teleparallel gravity.

The total energy matches the ADM energy when integrated over space.

Energy inside a Schwarzschild black hole can be explicitly calculated.

Abstract

In the framework of the teleparallel equivalent of general relativity the energy density of asymptoticaly flat gravitational fields can be naturally and unambiguously defined. Upon integration of the energy density over the whole three dimensional space we obtain the ADM energy. We use this energy density to calculate the energy inside a Schwarzschild black hole.