A closer glance at black hole pair creation

TL;DR

This paper investigates the symmetries and conserved charges of accelerated black hole horizons in the $C$-metric, revealing an infinite set of symmetries and their implications for black hole pair creation processes.

Contribution

It demonstrates the presence of infinite symmetries near black hole horizons in the $C$-metric and derives the superrotated, supertranslated geometries with conserved charges.

Findings

Identification of infinite symmetries in near horizon geometries.

Derivation of superrotated and supertranslated $C$-metric solutions.

Calculation of associated conserved charges for these symmetries.

Abstract

We consider accelerated black hole horizons with and without defects. These horizons appear in the $C$-metric solution to Einstein equations and in its generalization to the case where external fields are present. These solutions realize a variety of physical processes, from the decay of a cosmic string by a black hole pair nucleation to the creation of a black hole pair by an external electromagnetic field. Here, we show that such geometries exhibit an infinite set of symmetries in their near horizon region, generalizing in this way previous results for smooth isolated horizons. By considering the limit close to both the black hole and the acceleration horizons, we show that a sensible set of asymptotic boundary conditions gets preserved by supertranslation and superrotation transformations. By acting on the geometry with such transformations, we derive the superrotated, supertranslated version of the $C$-metric and compute the associated conserved charges.