General relativistic tidal heating for the M$\o$ller 58 pseudotensor

TL;DR

This paper re-examines the relativistic tidal heating calculation using Møller's pseudotensor, confirming its validity under certain conditions and extending the analysis to black hole scenarios beyond Newtonian physics.

Contribution

It clarifies the conditions under which Møller's pseudotensor yields correct tidal heating results and extends the analysis to black hole cases.

Findings

Møller pseudotensor agrees with expected tidal heating when mass is constant.

Favata's previous result was based on an illegitimate assumption of time-dependent mass.

Extension of tidal heating analysis to black hole scenarios.

Abstract

In his study of tidal stabilization of fully relativistic neutron stars Thorne showed that the fully relativistic expression for tidal heating is the same as in non-relativistic Newtonian theory. Furthermore, Thorne also noted that this tidal heating must be independent of how one localizes gravitational energy and is unambiguously given by that expression. Favata calculated the tidal heating for a number of classical gravitational pseudotensors including that of M$\o$ller, and obtained the result that all of them produced the same (Newtonian) value. After a re-examination of the calculation using the M$\o$ller pseudotensor we find that indeed this pseudotensor gives the desired result under the condition that the mass $M$ is a constant, while Favata considered $M$ as being time dependent, which is illegitimate since it violates the harmonic gauge condition, which he used. Moreover, we carry on to consider this M$\o$ller pseudtensor even in a black hole situation, i.e., beyond Newtonian physics.