  We study self-interacting massive scalar field theory in static spacetimes
with a bifurcate Killing horizon and a wedge reflection. In this theory the
Hartle-Hawking state is defined to have the $N$-point correlation functions
obtained by analytically continuing those in the Euclidean theory, whereas the
double Kubo-Martin-Schwinger (KMS) state is the pure state invariant under the
Killing flow and the wedge reflection which is regular on the bifurcate Killing
horizon and reduces to the thermal state at the Hawking temperature in each of
the two static regions. We demonstrate in the Schwinger-Keldysh operator
formalism of perturbation theory the equivalence between the Hartle-Hawking
state and the double KMS state with the Hawking temperature, which was shown
before by Jacobson in the path-integral framework.
