Exact Solutions for the Intrinsic Geometry of Black Hole Coalescence

TL;DR

This paper presents exact analytical solutions for the intrinsic geometry of black hole event horizons during coalescence, matching numerical simulations and offering insights into horizon shapes and the hoop conjecture.

Contribution

It introduces a conformal rescaling method for describing black hole horizons, reproducing complex shapes like pair-of-pants and toroidal horizons analytically.

Findings

Reproduces pair-of-pants horizon shape in head-on black hole collisions.

Models toroidal horizons in collapsing rotating clusters.

Provides a framework for analyzing white hole fission horizons.

Abstract

We describe the null geometry of a multiple black hole event horizon in terms of a conformal rescaling of a flat space null hypersurface. For the prolate spheroidal case, we show that the method reproduces the pair-of-pants shaped horizon found in the numerical simulation of the head-on-collision of black holes. For the oblate case, it reproduces the initially toroidal event horizon found in the numerical simulation of collapse of a rotating cluster. The analytic nature of the approach makes further conclusions possible, such as a bearing on the hoop conjecture. From a time reversed point of view, the approach yields a description of the past event horizon of a fissioning white hole, which can be used as null data for the characteristic evolution of the exterior space-time.