Quantum Stability of (2+1)-Spacetimes with Non-Trivial Topology

TL;DR

This paper examines quantum fields in (2+1)-dimensional universes with complex topologies, analyzing stability and divergences, and finds that certain cusps cause quantum instability, with implications for multi-black hole models.

Contribution

It investigates quantum stability in (2+1)-dimensional spacetimes with non-trivial topologies, focusing on cusp effects and their impact on quantum fields.

Findings

Cusps without singularities cause quantum divergences.

Negative curvature does not lead to topological divergence.

Certain cusps induce quantum instability.

Abstract

Quantum fields are investigated in the (2+1)-open-universes with non-trivial topologies by the method of images. The universes are locally de Sitter spacetime and anti-de Sitter spacetime. In the present article we study spacetimes whose spatial topologies are a torus with a cusp and a sphere with three cusps as a step toward the more general case. A quantum energy momentum tensor is obtained by the point stripping method. Though the cusps are no singularities, the latter cusps cause the divergence of the quantum field. This suggests that only the latter cusps are quantum mechanically unstable. Of course at the singularity of the background spacetime the quantum field diverges. Also the possibility of the divergence of topological effect by a negative spatial curvature is discussed. Since the volume of the negatively curved space is larger than that of the flat space, one see so many images of a single source by the non-trivial topology. It is confirmed that this divergence does not appear in our models of topologies. The results will be applicable to the case of three dimensional multi black hole\cite{BR}.