What Happens to Apparent Horizons in a Binary Black Hole Merger?

TL;DR

This paper investigates the evolution and fate of apparent horizons during a head-on merger of two non-spinning black holes, revealing their temporary persistence and eventual annihilation through a new computational method.

Contribution

It introduces a novel shooting method for locating MOTSs and clarifies the role of the stability operator in identifying black hole boundaries during mergers.

Findings

Original horizons persist temporarily after common horizon formation.

Inner and outer common horizons vanish independently through unstable MOTSs.

New method improves the detection of marginally outer trapped surfaces.

Abstract

We resolve the fate of the two original apparent horizons during the head-on merger of two non-spinning black holes. We show that following the appearance of the outer common horizon and subsequent inter-penetration of the original horizons, they continue to exist for a finite period of time before they are individually annihilated by unstable MOTSs. The inner common horizon vanishes in a similar, though independent, way. This completes the understanding of the analogue of the event horizon's "pair of pants" diagram for the apparent horizon. Our result is facilitated by a new method for locating marginally outer trapped surfaces (MOTSs) based on a generalized shooting method. We also discuss the role played by the MOTS stability operator in discerning which among a multitude of MOTSs should be considered as black hole boundaries.