Conformal mapping of Unruh temperature

TL;DR

This paper explores how conformal mappings relate the Unruh temperature experienced by observers in different spacetime regions, revealing that the temperature depends on the conformal factor and explaining why finite-lifetime observers perceive vacuum as thermal.

Contribution

It extends the conformal mapping framework to relate Unruh temperature in wedge and double-cone regions, providing a mathematical explanation for thermal perception in finite-lifetime observers.

Findings

Unruh temperature is proportional to the inverse of the conformal factor.

The mapping explains why observers with finite lifetime perceive vacuum as thermal.

Previous results on diamond's temperature are generalized through conformal mapping.

Abstract

Thanks to a local interpetation of the KMS condition, the mapping from (unbounded) wedge regions of Minkowski space-time to (bounded) double-cone regions is extended to the Unruh temperature associated to relevant observers in both regions. A previous result, the diamond's temperature, is shown to be proportional to the inverse of the conformal factor (Weyl rescaling of the metric) of this map. One thus explains from a mathematical point of view why an observer with finite lifetime experiences the vacuum as a thermal state whatever his acceleration, even vanishing.