General relativistic tidal heating for Moller pseudotensor

TL;DR

This paper investigates the relativistic tidal heating using the Moller pseudotensor and finds that, contrary to previous claims, it does not produce a tidal heating value, challenging the pseudotensor independence of the phenomenon.

Contribution

It demonstrates that the Moller pseudotensor does not yield a tidal heating value, questioning the universality of pseudotensor independence in relativistic tidal heating.

Findings

Moller pseudotensor yields no tidal heating value.

Relativistic tidal heating may depend on the choice of pseudotensor.

Pseudotensor independence holds only for Freud type superpotentials.

Abstract

Thorne elucidated that the relativistic tidal heating is the same as the Newtonian theory. Moreover, Thorne also claimed that the tidal heating is independent of how one localizes gravitational energy and is unambiguously given by a certain formula. Purdue and Favata calculated the tidal heating for different classical pseudotensors including Moller and obtained the results all matched with the Newtonian perspective. After re-examined this Moller pseudotensor, we find that there does not exist any tidal heating value. Thus we claim that the relativistic tidal heating is pseudotensor independent under the condition that if the peusdotensor is a Freud typed superpotential.