Casimir energy and variational methods in AdS spacetime

TL;DR

This paper investigates the Casimir energy in AdS spacetime using variational methods, revealing an unstable mode at zero temperature that can be stabilized, with implications for foam-like space structures.

Contribution

It introduces a variational approach to compute energy differences in AdS spaces and identifies an unstable mode that can be stabilized, advancing understanding of quantum effects in curved spacetime.

Findings

Unstable mode at zero temperature in AdS spacetime

Stabilization of the mode via boundary reduction

Implications for foam-like space structures

Abstract

Following the subtraction procedure for manifolds with boundaries, we calculate by variational methods, the Schwarzschild-Anti-de Sitter and the Anti-de Sitter space energy difference. By computing the one loop approximation for TT tensors we discover the existence of an unstable mode at zero temperature, which can be stabilized by the boundary reduction method. Implications on a foam-like space are discussed.