Gravitational energy of a Schwarzschild black hole

TL;DR

This paper uses a new gravitational energy momentum tensor to evaluate the distribution of gravitational energy in a Schwarzschild black hole, finding it resides entirely outside the horizon.

Contribution

It introduces a novel gravitational energy momentum tensor and applies it to analyze energy distribution in Schwarzschild black holes, contrasting with existing teleparallel gravity approaches.

Findings

All gravitational energy is outside the horizon.

No gravitational energy inside the horizon.

Comparison with teleparallel gravity energy tensor.

Abstract

In a previous paper, we proposed a new gravitational energy momentum tensor. Here we use this tensor to evaluate the gravitational energies both inside and outside the horizon of a Schwarzschild black hole. Our results show that all of the gravitational energy exists outside the horizon, and that there is no gravitational energy inside the horizon. We comment on a relation with our gravitational energy momentum tensor and another one which is proposed in a teleparallel gravity.