The Unruh state for massless fermions on Kerr spacetime and its Hadamard property

TL;DR

This paper rigorously constructs the Unruh state for massless fermions on Kerr spacetime, proving its thermal and Hadamard properties, which are crucial for understanding quantum fields in rotating black hole backgrounds.

Contribution

It provides a rigorous definition and analysis of the Unruh state for massless Dirac fields on Kerr spacetime, including its thermal and Hadamard characteristics.

Findings

Unruh state is asymptotically thermal at Hawking temperature on the horizon.

The state is shown to be pure and Hadamard in the exterior and interior regions.

Utilizes advanced scattering theory and microlocal analysis techniques.

Abstract

We give a rigorous definition of the Unruh state in the setting of massless Dirac fields on slowly rotating Kerr spacetimes. In the black hole exterior region, we show that it is asymptotically thermal at Hawking temperature on the past event horizon. Furthermore, we demonstrate that in the union of the exterior and interior regions, the Unruh state is pure and Hadamard. The main ingredients are the H\"afner-Nicolas scattering theory, new microlocal estimates for characteristic Cauchy problems and criteria on the level of square-integrable solutions.