The renormalized stress tensor in Kerr space-time: general results

TL;DR

This paper establishes general constraints on the renormalized stress tensor in Kerr space-time, analyzes various vacuum states, and discusses the challenges in defining a Hartle-Hawking-like state.

Contribution

It derives universal conditions for the stress tensor in Kerr space-time and examines the properties and limitations of different vacuum states.

Findings

Constraints on stress tensor form derived from physical principles.

Analysis of the Unruh vacuum at horizon and infinity.

Discussion on the non-existence of a vacuum empty at both past and future null infinity.

Abstract

We derive constraints on the form of the renormalized stress tensor for states on Kerr space-time based on general physical principles: symmetry, the conservation equations, the trace anomaly and regularity on (sections of) the event horizon. This is then applied to the physical vacua of interest. We introduce the concept of past and future Boulware vacua and discuss the non-existence of a state empty at both scri- and scri+. By calculating the stress tensor for the Unruh vacuum at the event horizon and at infinity, we are able to check our earlier conditions. We also discuss the difficulties of defining a state equivalent to the Hartle-Hawking vacuum and comment on the properties of two candidates for this state.