Hessling's Quantum Equivalence Principle and the Temperature of an Extremal Reissner-Nordstr\"{o}m Black Hole

TL;DR

This paper examines Hessling's quantum equivalence principle in the context of extremal Reissner-Nordström black holes, concluding that only the vacuum state with zero temperature is physically acceptable.

Contribution

It applies Hessling's improvement of the Haag, Narnhofer, and Stein principle to extremal R-N black holes, demonstrating the uniqueness of the zero-temperature vacuum state.

Findings

Only the R-N vacuum state is physically sensible under the principle.

The temperature of the extremal R-N black hole is confirmed to be zero.

The quantum equivalence principle constrains the state selection near extremal black holes.

Abstract

The Hessling improvement of the Haag, Narnhofer and Stein principle is analysed in the case of a massless scalar field propagating outside of an extremal R-N black hole. It is found that this sort of ``Quantum (Einstein's) Equivalence Principle'' selects only the R-N vacuum as a physically sensible state, i.e., it selects the temperature $T=0$ only.