Hawking radiation for Dirac spinors on the RP^3 geon

TL;DR

This paper investigates the Hawking radiation effect for Dirac spinors on the RP^3 geon, revealing how different spin structures influence the vacuum states and their thermal properties, with implications for topologically nontrivial spacetimes.

Contribution

It provides the first analysis of Hawking radiation for Dirac fermions on the RP^3 geon, including explicit Bogolubov transformations and distinctions between vacua based on spin structures.

Findings

Two distinct Hartle-Hawking-like vacua depending on spin structure.

Both vacua appear thermal to certain restricted operators.

Explicit Bogolubov transformation for massive Dirac fermions in Minkowski space.

Abstract

We analyse the Hawking(-Unruh) effect for a massive Dirac spinor on the Z_2 quotient of Kruskal spacetime known as the RP^3 geon. There are two distinct Hartle-Hawking-like vacua, depending on the choice of the spin structure, and suitable measurements in the static region (which on its own has only one spin structure) distinguish these two vacua. However, both vacua appear thermal in the usual Hawking temperature to certain types of restricted operators, including operators with support in the asymptotic future (or past). Similar results hold in a family of topologically analogous flat spacetimes, where we show the two vacua to be distinguished also by the shear stresses in the zero-mass limit. As a by-product, we display the explicit Bogolubov transformation between the Rindler-basis and the Minkowski-basis for massive Dirac fermions in four-dimensional Minkowski spacetime.