Angular Momentum for Black Hole Binaries in Numerical Relativity

TL;DR

This paper introduces a new expression for the orbital angular momentum of binary black holes in numerical relativity, enabling better understanding of angular momentum transfer during inspiral and merger phases.

Contribution

It formulates an orbital angular momentum expression valid at small separations, bridging numerical relativity and perturbation methods for Kerr black holes.

Findings

Expression agrees well with particle-perturbation results

Enables analysis of angular momentum transfer in black hole binaries

Facilitates study of tidal coupling effects

Abstract

The extensive catalog of waveforms, with details of binary black hole inspiral and merger, offer an opportunity to understand black hole interactions beyond the large separation regime. We envision a research program that focuses on the transfer of angular momentum from spin of the individual holes to the orbital angular momentum and the role of tidal coupling in the process. That analysis will require the formulation of an expression for the orbital angular momentum of a binary, an expression that is useful at small separations, since that regime is well out of the range of Newtonian approximations and is where tidal coupling should be most interesting. We report here such an expression, a binary orbital angular momentum based on numerical relativity results for quasi-circular orbits, that agrees remarkably well with a similar quantity constructed with particle-perturbation techniques for the Kerr geometry.