Quantum fields theory at finite temperature in curved space-times with the Killing horizon

It is known that an observer uniformly accelerated through the Minkowski vacuum experiences a thermal flux with an Unruh temperature. It will be shown that this effect does not lead to the appearance of a Debye mass. At the same time, consideration of the Bose gas for exact modes with an arbitrary temperature near the horizon of a black hole leads to the appearance of a Debye mass, which is significantly different from the physical mass. I will show that there is a difference between the partition function and the Euclidean path integral in space-times with the Killing horizon. I will also show that thermal effects in the static patch of de Sitter space-time lead to a "phase transition" at the level of correlation functions and partition function.