Horizon Surface Gravity in Corotating Black Hole Binaries

TL;DR

This paper investigates the surface gravity of corotating black hole binaries, confirming the zeroth law and demonstrating strong agreement between numerical, post-Newtonian, and perturbative predictions across various mass ratios.

Contribution

It provides the first detailed numerical analysis of surface gravity in corotating black hole binaries using quasi-equilibrium initial data and compares results with analytical theories.

Findings

Surface gravity is constant on each horizon component at sub-percent accuracy.

Numerical results agree well with 4PN and linear perturbation theory predictions.

Black hole perturbation theory remains valid beyond extreme mass ratios.

Abstract

For binary systems of corotating black holes, the zeroth law of black hole mechanics states that the surface gravity is constant over each component of the horizon. Using the approximation of a conformally flat spatial metric, we compute sequences of quasi-equilibrium initial data for corotating black hole binaries with irreducible mass ratios in the range 10:1-1:1. For orbits outside the innermost stable one, the surface gravity is found to be constant on each component of the apparent horizon at the sub-percent level. We compare those numerical results to the analytical predictions from post-Newtonian theory at the fourth (4PN) order and from black hole perturbation theory to linear order in the mass ratio. We find a remarkably good agreement for all mass ratios considered, even in the strong-field regime. In particular, our findings confirm that the domain of validity of black hole perturbative calculations appears to extend well beyond the extreme mass-ratio limit.