Divergence of a quantum thermal state on Kerr space-time

TL;DR

This paper proves that any isotropic quantum stress tensor on Kerr space-time must diverge at the velocity of light surface, highlighting issues with defining a Hartle-Hawking vacuum in rotating black holes.

Contribution

It provides a simple proof using conservation equations that quantum stress tensors in Kerr space-time diverge at the light surface, clarifying the limitations of vacuum states.

Findings

Quantum stress tensor diverges at the light surface in Kerr space-time.

No true Hartle-Hawking vacuum exists for Kerr black holes.

The divergence is linked to the rotation and isotropy conditions.

Abstract

We present a simple proof, using the conservation equations, that any quantum stress tensor on Kerr space-time which is isotropic in a frame which rotates rigidly with the angular velocity of the event horizon must be divergent at the velocity of light surface. We comment on our result in the light of the absence of a `true Hartle-Hawking' vacuum for Kerr.