The Renormalized Stress Tensor in Kerr Space-Time: Numerical Results for the Hartle-Hawking Vacuum

TL;DR

This paper investigates the Hartle-Hawking vacuum in Kerr spacetime, showing that its pathology is due to rigid rotation and that a mirror can create a well-behaved state with thermal properties at the Hawking temperature.

Contribution

It demonstrates that removing the problematic region with a mirror yields a physically consistent state with thermal properties matching the Hartle-Hawking vacuum.

Findings

Pathology linked to rigid rotation of the state.

Introducing a mirror removes the problematic region.

The stress tensor matches a thermal distribution at Hawking temperature.

Abstract

We show that the pathology which afflicts the Hartle-Hawking vacuum on the Kerr black hole space-time can be regarded as due to rigid rotation of the state with the horizon in the sense that when the region outside the speed-of-light surface is removed by introducing a mirror, there is a state with the defining features of the Hartle-Hawking vacuum. In addition, we show that when the field is in this state, the expectation value of the energy-momentum stress tensor measured by an observer close to the horizon and rigidly rotating with it corresponds to that of a thermal distribution at the Hawking temperature rigidly rotating with the horizon.