A practical formula for the radiated angular momentum

TL;DR

This paper introduces a straightforward formula to calculate radiated angular momentum from gravitational wave data, validated through simulations of black-hole binaries with consistent results.

Contribution

It provides a new, practical formula for computing radiated angular momentum using spin-weighted spherical harmonics of the Weyl scalar psi_4, tested on black-hole binary simulations.

Findings

The formula accurately measures radiated angular momentum.

Results agree with changes in remnant spins and initial angular momentum.

Validated across multiple binary configurations.

Abstract

We present a simple formula for the radiated angular momentum based on a spin-weighted spherical harmonic decomposition of the Weyl scalar psi_4 representing outgoing radiation in the Kinnersley tetrad. We test our formula by measuring the radiated angular momentum from three simulations of non-spinning equal-mass black-hole binary with orbital angular momentum aligned along the x, y, and z axes respectively. We find that the radiated angular momentum agrees with the differences in the remnant horizon spins and the initial angular momentum for each system.