Quantized Temperatures Spectra in Curved Spacetimes

TL;DR

This paper demonstrates that scalar fields in certain curved spacetimes exhibit a discrete set of allowed temperatures, specifically odd multiples of a fundamental temperature, with explicit constructions provided for their two-point functions.

Contribution

It introduces the concept of quantized temperature spectra in curved spacetimes and constructs explicit two-point functions for each allowed temperature, extending previous static metric analyses.

Findings

Discrete temperature spectra exist in de Sitter, Kruskal, and Rindler spacetimes.

Explicit two-point functions are constructed for each temperature.

Results apply to a broad class of static metrics with bifurcate Killing horizons.

Abstract

We consider the thermal properties of a scalar field theory on curved spacetimes. In particular, we argue for the existence in the de Sitter, Kruskal and Rindler manifolds of a discrete spectrum of allowed temperatures (the odd multiples of a fundamental one). For each temperature we give an explicit construction of the relative two point function in terms of the lowest temperature one. These results are actually valid for a wider class of static metrics with bifurcate Killing horizons, originally studied by Sewell. Some comments on the interpretation of our results are given.