Note on Hartle-Hawking vacua

The purpose of this Rapid Communication 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 a bifurcate Killing horizon admitting a regular Euclidean section. These states, for free or interacting fields, are defined by a Euclidean functional integral on half the Euclidean section. The emphasis is on generality, and the arguments are simple but formal.