Casimir energy and black hole pair creation in Schwarzschild-de Sitter spacetime

TL;DR

This paper calculates the energy difference between Schwarzschild-de Sitter and de Sitter spaces, finds an unstable mode indicating potential black hole pair creation, and discusses implications for a foam-like universe.

Contribution

It introduces a variational method to compute energy differences and identifies an unstable mode in Schwarzschild-de Sitter space, advancing understanding of black hole pair creation.

Findings

Existence of an unstable mode in Schwarzschild-de Sitter space

Energy difference computed via variational methods

Implications for foam-like spacetime structures

Abstract

Following the subtraction procedure for manifolds with boundaries, we calculate by variational methods, the Schwarzschild-de Sitter and the de Sitter space energy difference. By computing the one loop approximation for TT tensors we discover the existence of an unstable mode even for the non-degenerate case. This result seems to be in agreement with the sub-maximal black hole pair creation of Bousso-Hawking. The instability can be eliminated by the boundary reduction method. Implications on a foam-like space are discussed.