Relativistic tidal heating of Hamiltonian quasi-local boundary expressions

TL;DR

This paper demonstrates that various Hamiltonian quasi-local boundary expressions consistently yield the same tidal heating result, confirming its uniqueness and highlighting fundamental differences from pseudo-tensor methods.

Contribution

It introduces a new Hamiltonian quasi-local boundary expression that confirms the uniqueness of tidal heating calculations and clarifies differences from pseudo-tensor approaches.

Findings

All methods agree with Newtonian results

Tidal heating is shown to be unique as predicted by Thorne

Pseudo-tensor and quasi-local methods are fundamentally different

Abstract

Purdue and Favata calculate the tidal heating used certain classical pseudotensors. Booth and Creighton employed the quasi-local mass formalism of Brown and York to demonstrate the same subject. All of them give the result matched with the Newtonian theory. Here we present another Hamiltonian quasi-local boundary expressions and all give the same desired value. This indicates that the tidal heating is unique as Thorne predicted. Moreover, we discovered that the pseudo-tensor method and quasi-local method are fundamentally different.