Imprints of Spacetime Topology in the Hawking-Unruh Effect

TL;DR

This paper explores how non-trivial spacetime topologies influence the Unruh and Hawking effects through Bogolubov transformations, stress tensor calculations, and particle detector responses, revealing topology-induced modifications in quantum field phenomena.

Contribution

It provides a detailed analysis of quantum effects in topologically non-trivial spacetimes, extending existing models to include various boundary conditions, spin structures, and detector responses.

Findings

Modifications to the Unruh effect due to spacetime topology.

Stress tensor expectation values depend on topology and boundary conditions.

Detector responses vary with spacetime topology and observer motion.

Abstract

The Unruh and Hawking effects are investigated on certain families of topologically non-trivial spacetimes using a variety of techniques. First we present the Bogolubov transformation between Rindler and Minkowski quantizations on two flat spacetimes with topology ${\R}^3\times{S^1}$ (M_0 and M_-) for massive Dirac spinors. The two inequivalent spin structures on each are considered. Results show modifications to the Minkowski space Unruh effect. This provides a flat space model for the Hawking effect on Kruskal and RP^3 geon black hole spacetimes which is the subject of the rest of this part. Secondley we present the expectation values of the stress tensor for massive scalar and spinor fields on $M_0$ and $M_-$, and for massive scalar fields on Minkowski space with a single infinite plane boundary, in the Minkowski-like vacua. Finally we investigate particle detector models. We investigate Schlicht's regularization of the Wightman function and extend it to an arbitrary spacetime dimension, to quotient spaces of Minkowski space, to non-linear couplings, to a massless Dirac field, and to conformally flat spacetimes. Secondly we present some detector responses, including the time dependent responses of inertial and uniformly accelerated detectors on $M_-$ and $M$ with boundary with motion perpendicular to the boundary. Responses are also considered for static observers in the exterior of the RP^3 geon and comoving observers in RP^3 de Sitter space, via those in the associated GEMS.