Probing thermal effects on static spacetimes with Unruh-DeWitt detectors

TL;DR

This paper investigates how thermal quantum effects influence static spacetimes using Unruh-DeWitt detectors, revealing the role of boundary conditions, spacetime dimension, and coupling in phenomena like Hawking effects and quantum fluctuations.

Contribution

It introduces a framework for analyzing thermal quantum effects on static spacetimes with various boundary conditions and constructs two-point functions for Lifshitz black holes.

Findings

Anti-Unruh/Hawking effects are absent in certain black hole spacetimes.

Boundary conditions critically affect quantum fluctuations near singularities.

Two-point functions for Lifshitz black holes are explicitly constructed.

Abstract

In the lack of a full-fledged theory of quantum gravity, I consider free, scalar, quantum fields on curved spacetimes to gain insight into the interaction between quantum and gravitational phenomena. I employ the Unruh-DeWitt detector approach to probe thermal, quantum effects on static, non-globally hyperbolic spacetimes. In this context, all physical observables depend on the choice of a boundary condition that cannot be singled-out, in general, without resorting to an experiment. Notwithstanding, the framework applied admits a large family of (Robin) boundary conditions and grants us physically-sensible dynamics and two-point functions of local Hadamard form. I discover that the anti-Unruh/Hawking effects are not manifest for thermal states on the BTZ black hole, nor on massless topological black holes of four dimensions. Whilst the physical significance of these statistical effects remains puzzling, my work corroborates their non-trivial relation with the KMS condition and reveals the pivotal influence of the spacetime dimension in their manifestation. On global monopoles, I find that for massless minimally coupled fields the transition rate, the thermal fluctuations and the energy density remain finite at the singularity only for Dirichlet boundary condition. For conformally coupled fields, although the energy density diverges for all boundary conditions, the transition rate and the thermal fluctuations vanish at the monopole; indicating that even if there is infinite energy, no spontaneous emission occur if the quantum field is not fluctuating. Moreover, I explicitly construct two-point functions for ground and thermal states on Lifshitz topological black holes, setting the ground for future explorations in this Lorentz breaking context.