The gauge invariance of general relativistic tidal heating

TL;DR

This paper demonstrates that in general relativity, the work done on a tidally interacting body is gauge-invariant, while the interaction energy depends on the choice of gauge, paralleling Newtonian gravitational energy localization.

Contribution

It clarifies the gauge invariance of tidal heating work and the gauge dependence of interaction energy in general relativity using the Landau-Lifshitz pseudotensor.

Findings

Work done on the body is gauge-invariant.

Interaction energy within the body's frame is gauge-dependent.

Results parallel Newtonian gravitational energy localization.

Abstract

When a self-gravitating body (e.g., a neutron star or black hole) interacts with an external tidal field (e.g., that of a binary companion), the interaction can do work on the body, changing its mass-energy. The details of this "tidal heating" are analyzed using the Landau-Lifshitz pseudotensor and the local asymptotic rest frame of the body. It is shown that the work done on the body is gauge-invariant, while the body-tidal-field interaction energy contained within the body's local asymptotic rest frame is gauge dependent. This is analogous to Newtonian theory, where the interaction energy is shown to depend on how one localizes gravitational energy, but the work done on the body is independent of that localization.