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

TL;DR

This paper investigates the quantum process of cosmic string breaking in de Sitter space, leading to black hole pair creation, by constructing instanton solutions and calculating the associated nucleation rates.

Contribution

It introduces explicit instanton solutions for black hole pair creation on a cosmic string in de Sitter space and computes the corresponding nucleation rates.

Findings

Derived explicit instanton solutions describing the process.

Calculated the pair creation rate and string nucleation probability.

Confirmed the rate is proportional to exp(S), with S as the black hole entropy.

Abstract

We analyze the quantum process in which a cosmic string breaks in a de Sitter (dS) background, and a pair of neutral or charged black holes is produced at the ends of the string. The energy to materialize and accelerate the pair comes from the positive cosmological constant and, in addition, from the string tension. The compact saddle point solutions without conical singularities (instantons) or with conical singularities (sub-maximal instantons) that describe this process are constructed through the analytical continuation of the dS C-metric. Then, we explicitly compute the pair creation rate of the process. In particular, we find the nucleation rate of a cosmic string in a dS background, and the probability that it breaks and a pair of black holes is produced. Finally we verify that, as occurs with pair production processes in other background fields, the pair creation rate of black holes is proportional to exp(S), where the gravitational entropy of the black hole, S, is given by one quarter of the area of the horizons present in the saddle point solution that mediates the process.