Coalescence of Kerr Black Holes: Binary Systems from GW150914 to GW170814

TL;DR

This paper models the energy and angular momentum transfer in binary Kerr black hole mergers, analyzing how gravitational waves carry away energy and spin, with applications to LIGO observations.

Contribution

It introduces an analytical and numerical framework for understanding gravitational wave energy and spin transfer in Kerr black hole mergers, consistent with particle absorption limits.

Findings

Final black holes acquire significant spin from orbital angular momentum.

Gravitational wave energy depends on effective spin-orbit interactions.

Application to LIGO events estimates angular momentum loss.

Abstract

We investigate the energy of the gravitational wave from a binary black hole merger by the coalescence of two Kerr black holes with an orbital angular momentum. The coalescence is constructed to be consistent with particle absorption in the limit in which the primary black hole is sufficiently large compared with the secondary black hole. In this limit, we analytically obtain an effective gravitational spin--orbit interaction dependent on the alignments of the angular momenta. Then, binary systems with various parameters including equal masses are numerically analyzed. According to the numerical analysis, the energy of the gravitational wave still depends on the effective interactions, as expected from the analytical form. In particular, we ensure that the final black hole obtains a large portion of its spin angular momentum from the orbital angular momentum of the initial binary black hole. To estimate the angular momentum released by the gravitational wave in the actual binary black hole, we apply our results to observations at the Laser Interferometer Gravitational-Wave Observatory: GW150914, GW151226, GW170104, GW170608, and GW170814.