The merger of a black hole with a cosmological horizon

TL;DR

This paper investigates the dynamic process of a black hole merging with a cosmological horizon in Schwarzschild-de Sitter spacetime, analyzing horizon geometry, caustics, and area growth, and connecting to known black hole mergers as the cosmological constant approaches zero.

Contribution

It introduces a model of black hole and cosmological horizon merger, extending previous work by replacing the large black hole with a cosmological horizon and analyzing the geometric and area evolution.

Findings

Horizon geometry evolves over time during merger.

Caustics play a significant role in the merger process.

Horizon area growth can be regularized in the zero cosmological constant limit.

Abstract

In recent years there have been many studies on exactly solvable black hole mergers, based on a model by Emparan and Martinez where the mass of one black hole is blown up to infinity. Here we replace the large black hole by a cosmological horizon, and study how it merges with a black hole in the Schwarzschild-de Sitter spacetime by considering an observer positioned at future null infinity. We describe the geometry of the horizon over time, including the role that caustics play in the merger process, and also examine the growth of the horizon area. We argue that in the limit of zero cosmological constant, the system reduces to the Emparan-Martinez Schwarzschild merger. This allows us to regularise the increase in the area during the merger, which otherwise diverges.