Some remarks on the Einstein and M{\o}ller pseudotensors for static and spherically-symmetric configurations

TL;DR

This paper explores the properties of Einstein and Møller pseudotensors in static, spherically symmetric systems, relating their hypotheses to source distributions, with examples including quantum-corrected black holes.

Contribution

It establishes connections between pseudotensor hypotheses and source distributions, providing simple proofs and analyzing quantum-corrected black holes.

Findings

Hypotheses by Yang, Radinschi, and Vagenas relate to source distributions.

Simple proofs demonstrate these relationships.

Quantum corrections to Schwarzschild black holes are discussed.

Abstract

It is shown that for the spherically-symmetric and static systems the hypotheses posed by Yang and Radinschi and by Vagenas can be related to the particular distribution of the source. Simple proofs are given and a number of examples are discussed with the special emphasis put on the quantum corrected Schwarzschild black hole.