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

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.

arXiv comment6 pages, 5 figures, V2: final version with several changes (including changed title)

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• Tidal deformation of dynamical horizons in binary black hole mergers
• Quasi-Local Black Hole Horizons: Recent Advances
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• Black holes and their horizons in semiclassical and modified theories of gravity