Cusp Formation in Merging Black Hole Horizons

TL;DR

This paper investigates the formation of cusps in black hole horizons during mergers, using numerical simulations to connect initial black hole properties with the final remnant through horizon analysis.

Contribution

It introduces a numerical study of cusp formation in merging black hole horizons and proposes a phenomenological model linking horizon features to initial conditions.

Findings

Cusps form in black hole horizons during mergers.

Mass and multipole moments exhibit specific behaviors at the cusp.

A phenomenological model relates cusp features to initial black hole parameters.

Abstract

An important question in binary black hole mergers is to connect properties of the remnant black hole to those of the two initial black holes. These properties include not only the final mass and spin of the remnant, but also higher multipoles and answers to other questions such as, for a given initial configuration, which quasi-normal modes of the final black hole are excited, and what are the amplitudes of these modes? Such questions have thus far been primarily addressed through a study of the emitted gravitational wave signal. In this paper we consider a different alternative, namely using quasi-local black hole horizons themselves to establish the link between the initial and final states. Recent work has elucidated the behavior of black hole horizons in a merger. Cusps forming in such otherwise smoothly evolving horizons have been shown to play a central role in connecting the two initially separate black holes with the final remnant. In the present work, we will discuss from a numerical perspective how such cusps form in detail for the head-on collision of two non-spinning black holes. We show how the mass and higher mass multipole moments behave at the cusp and suggest a phenomenological model.