The Innermost Stable Circular Orbit of Binary Black Holes

TL;DR

This paper presents a new method for constructing binary black hole solutions in general relativity, focusing on accurately locating the innermost stable circular orbit and comparing different manifold structures.

Contribution

It introduces a novel approach to model binary black holes in quasicircular orbit using a three-sheeted manifold, and assesses the impact on the innermost stable orbit location.

Findings

The new method confirms previous results on the ISCO location.

The manifold structure has minimal effect on the ISCO.

The approach allows for arbitrary black hole momenta.

Abstract

We introduce a new method to construct solutions to the constraint equations of general relativity describing binary black holes in quasicircular orbit. Black hole pairs with arbitrary momenta can be constructed with a simple method recently suggested by Brandt and Bruegmann, and quasicircular orbits can then be found by locating a minimum in the binding energy along sequences of constant horizon area. This approach produces binary black holes in a "three-sheeted" manifold structure, as opposed to the "two-sheeted" structure in the conformal-imaging approach adopted earlier by Cook. We focus on locating the innermost stable circular orbit and compare with earlier calculations. Our results confirm those of Cook and imply that the underlying manifold structure has a very small effect on the location of the innermost stable circular orbit.