Construction of the Unruh State for a Real Scalar Field on the Kerr-de Sitter Spacetime

TL;DR

This paper constructs a physically meaningful Hadamard state, extending the Unruh state, for a scalar field in Kerr-de Sitter spacetimes with small angular momentum and cosmological constant, aiding quantum field analysis in such backgrounds.

Contribution

It provides the first rigorous construction of an Unruh state extension as a Hadamard state in Kerr-de Sitter spacetimes with small parameters.

Findings

Successfully extended the Unruh state to Kerr-de Sitter spacetime.

Proved the state is Hadamard outside and inside the black hole up to the inner horizon.

Offers a new tool for quantum field theory in rotating black hole backgrounds.

Abstract

The study of physical effects of quatum fields in black hole spacetimes, which is related to questions such as the validity of the strong cosmic censorship conjecture, requires a Hadamard state describing the physical situation. Here, we consider the theory of a free scalar field on a Kerr-de Sitter spacetime, focussing on spacetimes with sufficiently small angular momentum of the black hole and sufficiently small cosmological constant. We demonstrate that an extension of the Unruh state, which describes the expected late-time behaviour in spherically symmetric gravitational collapse, can be rigorously constructed for the free scalar field on such Kerr-de Sitter spacetimes. In addition, we show that this extension of the Unruh state is a Hadamard state in the black hole exterior and in the black hole interior up to the inner horizon. This provides a physically motivated Hadamard state for the study of free scalar fields in rotating black hole spacetimes.