General relativistic tidal work for Papapetrou, Weinberg and Goldberg pseudotensors

TL;DR

This paper demonstrates that various classical gravitational pseudotensors, including Papapetrou, Weinberg, and Goldberg, yield consistent relativistic tidal work results, supporting the pseudotensor independence of tidal work in general relativity.

Contribution

It extends the analysis of tidal work to additional pseudotensors and constructs a generalized pseudotensor, confirming the pseudotensor independence of tidal work.

Findings

All considered pseudotensors produce the same tidal work as Newtonian theory.

A generalized pseudotensor with higher order terms also agrees with Thorne's prediction.

Most classical pseudotensors satisfy the inside matter condition, except Møller.

Abstract

In 1998 Thorne claimed that all pseudotensors give the same tidal work as the Newtonian theory. In 1999, Purdue used the Landau-Lifshitz pseudotensor to calculate the tidal heating and the result matched with the Newtonian gravity. Soon after in 2001, Favata employed the same method to examine the Einstein, Bergmann-Thomson and M{\o}ller pseudotensors, all of them give the same result as Purdue did. Inspired by the work of Purdue and Favata, for the completeness, here we manipulate the tidal work for Papapetrou, Weinberg and Goldberg pseudotensors. We obtained the same tidal work as Purdue achieved. In addition, we emphasize that a suitable gravitational energy-momentum pseudotensor requires fulfill the inside matter condition and all of the classical pseudotensors pass this test except M$\o$ller. Moreover, we constructed a general pseudotesnor which is modified by 13 linear artificial higher order terms combination with Einstein pseudotensor. We find that the result agrees with Thorne's prediction, i.e., relativistic tidal work is pseudotensor independent.