Evolution of creases on the event horizon of a black hole merger

TL;DR

This paper analyzes the geometric evolution of creases on the event horizon during a black hole merger in the infinite mass ratio limit, revealing finite crease area, diverging gravitational entropy, and caustic structures modeled as an astroid tube.

Contribution

It provides a detailed geometric and perturbative analysis of creases and caustics on the event horizon in a black hole merger, extending previous models to higher order.

Findings

Creases on the event horizon have finite area.

Gravitational entropy expression diverges at merger.

Caustics form an 'astroid tube' structure in spacetime.

Abstract

A generic black hole merger occurs through a restructuring of creases (sharp edges) on the event horizon. This process is studied for a black hole merger in the limit of infinite mass ratio, for which constructing the event horizon reduces to finding a null hypersurface that asymptotes to a Rindler horizon in the Kerr spacetime. Geometrical properties of the creases on this horizon are determined and the results are compared with the predictions of an exact local description of the event horizon in a generic merger. The crease set is shown to have finite area. A recently proposed expression for the gravitational entropy of a crease is shown to diverge at the instant of merger. Caustics on (and off) the event horizon are determined by exploiting the correspondence with the problem of gravitational lensing by a Kerr black hole. Caustics form an "astroid tube" in spacetime, two edges of which lie on the event horizon of the merger. Perturbative expressions for the location of this tube are presented, extending previous work to much higher perturbative order.