Dynamic black holes through gravitational collapse: Analysis of multipole moment of the curvatures on the horizon

TL;DR

This paper investigates the properties of rapidly rotating dynamic black holes formed by gravitational collapse, analyzing their multipole moments and how they approach Kerr black hole characteristics through numerical simulations.

Contribution

It demonstrates the formation of highly spinning black holes via collapse of differentially rotating stars and analyzes horizon multipole moments to understand their dynamic approach to Kerr black holes.

Findings

Dynamic black holes can reach spins up to J/M^2 ~ 0.95.

Different angular momentum definitions yield consistent results.

Dynamic black holes approach Kerr characteristics within a rotational period.

Abstract

We have investigated several properties of rapidly rotating dynamic black holes generated by gravitational collapse of rotating relativistic stars. At present, numerical simulations of the binary black hole merger are able to produce a Kerr black hole of J_final / M_final^2 up to = 0.91, of gravitational collapse from uniformly rotating stars up to J_final / M_final^2 ~ 0.75, where J_final is the total angular momentum and M_final the total gravitational mass of the hole. We have succeeded in producing a dynamic black hole of spin J_final / M_final^2 ~ 0.95 through the collapse of differentially rotating relativistic stars. We have investigated those dynamic properties through diagnosing multipole moment of the horizon, and found the following two features. Firstly, two different definitions of the angular momentum of the hole, the approximated Killing vector approach and dipole moment of the current multipole approach, make no significant difference to our computational results. Secondly, dynamic hole approaches a Kerr by gravitational radiation within the order of a rotational period of an equilibrium star, although the dynamic hole at the very forming stage deviates quite far from a Kerr. We have also discussed a new phase of quasi-periodic waves in the gravitational waveform after the ringdown in terms of multipole moment of the dynamic hole.