Pair Creation of Black Holes in Anti-de Sitter Space Background (I)

TL;DR

This paper investigates the quantum pair creation of Schwarzschild-anti-de Sitter black holes using a constrained instanton approach, finding that the creation probability relates to the black hole entropy, with implications for open and closed pair creation scenarios.

Contribution

It introduces a complex constrained instanton method to analyze black hole pair creation in AdS space, linking creation probability to black hole entropy.

Findings

Creation probability is exponential of negative black hole entropy.

Black hole entropy is proportional to horizon area.

Method applies to both open and closed black hole pair creation.

Abstract

For a spherically symmetric vacuum model with a negative cosmological constant, a complex constrained instanton is considered as the seed for the quantum pair creation of Schwarzschild-anti-de Sitter black holes. The relative creation probability is found to be the exponential of the negative of the black hole entropy. The black hole entropy is known to be one quarter of the black hole horizon area. In the absence of a general no-boundary proposal for open creation, the constrained instanton approach is used in treating both the open and closed pair creations of black holes.