Quasi-equilibrium binary black hole sequences for puncture data derived from helical Killing vector conditions

TL;DR

This paper constructs binary black hole sequences using puncture data based on helical Killing vector conditions, assuming constant puncture mass and quasi-circular orbits, and finds consistent horizon mass and stable orbit predictions.

Contribution

It introduces a method to generate binary black hole sequences satisfying specific mass and orbit conditions, applicable to non-spinning equal mass binaries and potentially more general cases.

Findings

Apparent horizon mass remains constant along the sequence.

Predicted innermost stable circular orbit aligns with effective potential results.

Method applicable to general binary black hole configurations.

Abstract

We construct a sequence of binary black hole puncture data derived under the assumptions (i) that the ADM mass of each puncture as measured in the asymptotically flat space at the puncture stays constant along the sequence, and (ii) that the orbits along the sequence are quasi-circular in the sense that several necessary conditions for the existence of a helical Killing vector are satisfied. These conditions are equality of ADM and Komar mass at infinity and equality of the ADM and a rescaled Komar mass at each puncture. In this paper we explicitly give results for the case of an equal mass black hole binary without spin, but our approach can also be applied in the general case. We find that up to numerical accuracy the apparent horizon mass also remains constant along the sequence and that the prediction for the innermost stable circular orbit is similar to what has been found with the effective potential method.