Improved next-to-leading order tidal heating and torquing of a Kerr black hole

TL;DR

This paper derives advanced formulas for energy and angular momentum fluxes across a Kerr black hole's horizon under tidal influences, improving accuracy to 1.5 post-Newtonian order for generic binary systems.

Contribution

It provides the first next-to-leading order calculations of tidal fluxes for rapidly rotating black holes in binary systems, extending previous extreme mass ratio results.

Findings

Flux expressions valid for arbitrary mass ratios.

Discrepancy found with previous extreme mass ratio results at 1.5PN order.

Results applicable to slowly-moving, quasi-circular binary orbits.

Abstract

We calculate the energy and angular momentum fluxes across the event horizon of a tidally deformed, rapidly rotating black hole to next-to-leading order in the curvature of the external spacetime. These are expressed in terms of tidal quadrupole moments and their time derivatives, which provide a characterization of a generic tidal environment. As an application of our results, we provide an expression for the energy and angular-momentum fluxes across the horizon when the black hole is a member of a binary system on a slowly-moving, quasi-circular orbit. Our expressions are accurate to 1.5 post-Newtonian order beyond the leading-order fluxes, but they are valid for arbitrary mass ratios. We compare our results to those previously obtained in the case of an extreme mass ratio binary, and find that they do not agree at the 1.5 post-Newtonian order. We investigate a number of possible sources for this discrepancy, but are ultimately unable to resolve it.