Pair creation of anti-de Sitter black holes on a cosmic string background

TL;DR

This paper studies the quantum creation of black hole pairs on a cosmic string in anti-de Sitter space, deriving explicit rates and analyzing how the process depends on black hole parameters and background curvature.

Contribution

It provides the first detailed analysis of black hole pair creation on a cosmic string in AdS space, including explicit instanton construction and rate calculations.

Findings

Pair creation rate is explicitly computed.

Nonextreme black holes are more likely to be produced than extreme ones.

The rate behavior is similar across AdS, flat, and de Sitter backgrounds.

Abstract

We analyze the quantum process in which a cosmic string breaks in an anti-de Sitter (AdS) background, and a pair of charged or neutral black holes is produced at the ends of the strings. The energy to materialize and accelerate the pair comes from the strings tension. In an AdS background this is the only study done in the process of production of a pair of correlated black holes with spherical topology. The acceleration $A$ of the produced black holes is necessarily greater than (|L|/3)^(1/2), where L<0 is the cosmological constant. Only in this case the virtual pair of black holes can overcome the attractive background AdS potential well and become real. The instantons that describe this process are constructed through the analytical continuation of the AdS C-metric. Then, we explicitly compute the pair creation rate of the process, and we verify that (as occurs with pair creation in other backgrounds) the pair production of nonextreme black holes is enhanced relative to the pair creation of extreme black holes by a factor of exp(Area/4), where Area is the black hole horizon area. We also conclude that the general behavior of the pair creation rate with the mass and acceleration of the black holes is similar in the AdS, flat and de Sitter cases, and our AdS results reduce to the ones of the flat case when L=0.