A remark on the quasilocal calculation of tidal heating: energy transfer through the quasilocal surface

TL;DR

This paper refines the quasilocal formalism for calculating tidal heating, revealing larger effects and correction terms that extend Einstein's quadrupole formula, enhancing understanding of energy transfer in gravitating systems.

Contribution

It introduces correction terms in the quasilocal energy calculation, extending previous results and providing a more accurate description of tidal heating effects.

Findings

Tidal heating effects are larger than previously estimated.

Identification of a bulk-to-boundary inflow term affecting energy calculations.

Extension of Einstein's quadrupole formula in the large sphere limit.

Abstract

In this note, using the quasilocal formalism of Brown and York, the flow of energy through a closed surface containing a gravitating physical system is calculated in a way that augments earlier results on the subject by Booth and Creighton. To this end, by performing a variation of the total gravitational Hamiltonian (bulk plus boundary part), it is shown that associated tidal heating and deformation effects generally are larger than expected. This is because this variation leads to previously unrecognized correction terms, including a bulk-to-boundary inflow term that does not appear in the original calculation of the time derivative of the Brown-York energy and leads to corrective extensions of Einstein's quadrupole formula in the large sphere limit.