A Note on Hartle-Hawking Vacua

TL;DR

This paper analyzes the properties of generalized Hartle-Hawking vacua in static spacetimes, establishing their regularity, thermality, and time independence using a path integral approach.

Contribution

It provides a general and formal framework for understanding the basic properties of Hartle-Hawking vacua in static spacetimes with bifurcate Killing horizons.

Findings

Hartle-Hawking vacua are regular at the horizon

They exhibit thermality and time independence

The states are defined via a path integral on half the Euclidean section

Abstract

The purpose of this note is to establish the basic properties--- regularity at the horizon, time independence, and thermality--- of the generalized Hartle-Hawking vacua defined in static spacetimes with bifurcate Killing horizon admitting a regular Euclidean section. These states, for free or interacting fields, are defined by a path integral on half the Euclidean section. The emphasis is on generality and the arguments are simple but formal.