A quasilocal calculation of tidal heating

TL;DR

This paper introduces a quasilocal formalism-based method for calculating energy flux and tidal heating in gravitating systems, demonstrating its application to gravitational waves and tidal interactions in non-stationary spacetimes.

Contribution

It presents the first application of the quasilocal formalism to non-stationary spacetimes, enabling analysis of tidal effects in isolated gravitational systems.

Findings

Calculated energy flux via gravitational waves near infinity.

Quantified tidal heating in a body under external tidal influence.

Demonstrated the formalism's applicability to non-stationary spacetimes.

Abstract

We present a method for computing the flux of energy through a closed surface containing a gravitating system. This method, which is based on the quasilocal formalism of Brown and York, is illustrated by two applications: a calculation of (i) the energy flux, via gravitational waves, through a surface near infinity and (ii) the tidal heating in the local asymptotic frame of a body interacting with an external tidal field. The second application represents the first use of the quasilocal formalism to study a non-stationary spacetime and shows how such methods can be used to study tidal effects in isolated gravitating systems.