Hadamard state in Schwarzschild-de Sitter spacetime

TL;DR

This paper constructs a Hadamard state in Schwarzschild-de Sitter spacetime using a bulk-to-boundary approach, which is invariant under symmetries but not globally defined, and differs from KMS states in single-horizon spacetimes.

Contribution

It introduces a new method to construct a Hadamard state in Schwarzschild-de Sitter spacetime that is symmetry-invariant but not globally defined, expanding understanding of quantum states in such backgrounds.

Findings

The state is invariant under spacetime symmetries.

The state is Hadamard but not a KMS state.

Construction uses bulk-to-boundary technique.

Abstract

We construct a state in the Schwarzschild-de Sitter spacetime which is invariant under the action of its group of symmetries. Our state is not defined in the whole Kruskal extension of this spacetime, but rather in a subset of the maximally extended conformal diagram. The construction is based on a careful use of the bulk-to-boundary technique. We will show that our state is Hadamard and that it is not a KMS state, differently from the case of states constructed in spacetimes containing only one event horizon.