Creation of a black hole pair with a domain wall

TL;DR

This paper investigates the creation of black hole pairs separated by a domain wall in a universe with a cosmological constant, analyzing the effects of charge on the pair creation rate and horizon area.

Contribution

The study constructs explicit solutions for charged and neutral black hole pairs with domain walls and compares their creation probabilities in different dimensions.

Findings

Charged black hole pair creation rate is always suppressed compared to neutral ones.

The Euclidean action equals minus the entropy, linking creation rate to horizon area.

Charged black holes have smaller horizon areas, explaining the lower creation rate.

Abstract

We study the creation of a black hole (BH) pair separated by a domain wall, in the presence of a cosmological constant. We construct the solution representing a BH pair with a domain wall and compute the Euclidean action to evaluate the probability of the pair creation in the background with a preexisting domain wall. The BHs can be either neutral or magnetically charged ones. We compare the results of the charged case with those of the neutral case with the same cosmological constant. We find that the production rate of a charged BH pair is always suppressed in comparison with that of the neutral one in both four and five dimensions, irrespective of the sign of the cosmological constant. The Euclidean action is equal to the minus of the entropy. Since the horizon area of a BH is decreased as the magnitude of its charge is increased in general, the decreasing creation rate can be understood in terms of the increasing charge. We obtain the explicit confirmation on the relation between the pair creation rate of the charged BHs and the area of horizons in both the four- and five-dimensional cases in the presence of a cosmological constant. The singularity of the domain wall universe with charged BHs, as distinct from that with neutral BHs, can be avoided.