Boulware state and semiclassical thermodynamics of black holes in a cavity

TL;DR

This paper investigates the quantum effects on black holes enclosed in a cavity, focusing on the Boulware state and how it modifies the Hawking temperature through vacuum polarization effects.

Contribution

It provides a new calculation of quantum corrections to Hawking temperature considering the Boulware state in a cavity setup.

Findings

Quantum correction to Hawking temperature proportional to the trace of the stress-energy tensor.

Boundary contributions dominate when the shell is close to the horizon.

Vacuum polarization effects significantly alter black hole thermodynamics.

Abstract

A black hole, surrounded by a reflecting shell, acts as an effective star-like object with respect to the outer region that leads to vacuum polarization outside, where the quantum fields are in the Boulware state. We find the quantum correction to the Hawking temperature, taking into account this circumstance. It is proportional to the integral of the trace of the total quantum stress-energy tensor over the whole space from the horizon to infinity. For the shell, sufficiently close to the horizon, the leading term comes from the boundary contribution of the Boulware state.