Notes on peculiarities of quantum fields in space-times with horizons

We consider massive scalar field theory on static four-dimensional space-times with horizons. We study the near horizon behaviour of the quantum expectation values of the stress-energy tensor operator for thermal state with generic temperatures. It turns out that the dependence of the expectation values on the temperature and tensor structure of the stress-energy tensor differs from the usual one in the Minkowski space-time. Moreover, for non-canonical temperatures these expectation values are divergent on the horizons. We also show that the Wightman functions have additional infrared peculiarities near the horizons.