General relativistic tidal heating for the Moller pseudotensor

TL;DR

This paper re-examines the calculation of tidal heating in general relativity using the Moller pseudotensor, concluding that tidal heating is pseudotensor independent only for pseudotensors derived from a Freud type superpotential.

Contribution

It clarifies the conditions under which relativistic tidal heating is pseudotensor independent, challenging previous results with the Moller pseudotensor.

Findings

No tidal heating with Moller pseudotensor in re-examination

Tidal heating is pseudotensor independent only for Freud type superpotential pseudotensors

Supports Thorne's assertion with a specific caveat

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 the tidal heating must be independent of how one localizes gravitational energy and is unambiguously given by that expression. Purdue and Favata calculated the tidal heating for a number of classical gravitational pseudotensors including that of Moller, and obtained the result that all of them produced the same (Newtonian) value. However, in a re-examination of the calculation using the Moller pseudotensor we find that there is no tidal heating. This leads us to the conclusion that Thorne's assertion needs a minor modification: the relativistic tidal heating is pseudotensor independent only if the pseudotensor is derived from a Freud type superpotential.