Exact Event Horizon of a Black Hole Merger

TL;DR

This paper provides an exact analytic description of the event horizon during a binary black hole merger in the extreme-mass-ratio limit, using elliptic functions to analyze its evolution and key features.

Contribution

It introduces an exact analytic model for the event horizon in the extreme-mass-ratio limit of black hole mergers, utilizing elliptic functions for precise characterization.

Findings

Explicit form of the event horizon in terms of elliptic functions.

Identification of caustic lines and horizon contact points.

Analysis of the horizon's time-evolution during merger.

Abstract

We argue that the event horizon of a binary black hole merger, in the extreme-mass-ratio limit where one of the black holes is much smaller than the other, can be described in an exact analytic way. This is done by tracing in the Schwarzschild geometry a congruence of null geodesics that approaches a null plane at infinity. Its form can be given explicitly in terms of elliptic functions, and we use it to analyze and illustrate the time-evolution of the horizon along the merger. We identify features such as the line of caustics at which light rays enter the horizon, and the critical point at which the horizons touch. We also compute several quantities that characterize these aspects of the merger.