Heating up an environment around black holes and inside de Sitter space

We study quantum fields on spacetimes having a bifurcate Killing horizon by allowing the possibility that left and right (ingoing and outgoing) modes have different temperatures. An example of such a state is the Unruh vacuum in a black hole background, in which ingoing modes are in the zero temperature state, while the outgoing ones arc at the Hawking temperature. We construct the corresponding Wightman functions and study their properties with arbitrary and different temperatures for both types of movers. We consider, in particular, the Rindler for both massless and massive fields, the static de Sitter, and Schwarzschild black hole backgrounds for massive fields. We find that in all three cases, when any of the temperatures arc different from the canonical one (Unruh, Hawking, and Gibbons-Hawking, correspondingly) the correlation functions have extra singularities at the horizon.