Dissipation in extreme-mass ratio binaries with a spinning secondary

TL;DR

This paper derives a new gravitational-wave flux balance law for extreme-mass ratio binaries with a spinning secondary, validated through analytical and numerical calculations in Kerr spacetime.

Contribution

It introduces a novel flux balance law accounting for a spinning secondary in extreme-mass ratio binaries, extending previous models to include spin effects.

Findings

The balance law holds for generic bound orbits in Kerr spacetime.

Explicit calculations for spin-aligned bodies on circular orbits around Schwarzschild black holes.

Validation of the law through both analytical post-Newtonian and numerical methods.

Abstract

We present the gravitational-wave flux balance law in an extreme mass-ratio binary with a spinning secondary. This law relates the flux of energy (angular momentum) radiated to null infinity and through the event horizon to the local change in the secondary's orbital energy (angular momentum) for generic (non-resonant) bound orbits in Kerr spacetime. As an explicit example we compute these quantities for a spin-aligned body moving on a circular orbit around a Schwarzschild black hole. We perform this calculation both analytically, via a high-order post-Newtonian expansion, and numerically in two different gauges. Using these results we demonstrate explicitly that our new balance law holds.