Notes on peculiarities of quantum fields in space-times with horizons

TL;DR

This paper investigates the behavior of quantum scalar fields near horizons in static space-times, revealing temperature-dependent divergences and infrared peculiarities that differ from flat space results.

Contribution

It provides a detailed analysis of the stress-energy tensor and Wightman functions near horizons, highlighting new infrared and temperature-dependent phenomena.

Findings

Expectation values depend on temperature and tensor structure differently than in Minkowski space.

Non-canonical temperatures lead to divergences on the horizons.

Wightman functions exhibit additional infrared peculiarities near horizons.

Abstract

We consider massive scalar field theory on static four-dimensional space-times with horizons. We study the near horizon behaviour of the quantum expectation values of the stress-energy tensor operator for thermal state with generic temperatures. It turns out that the dependence of the expectation values on the temperature and tensor structure of the stress-energy tensor differs from the usual one in the Minkowski space-time. Moreover, for non-canonical temperatures these expectation values are divergent on the horizons. We also show that the Wightman functions have additional infrared peculiarities near the horizons.