On the backreaction issue for the black hole in de Sitter space-time

We consider quantum real massive scalar field in the de Sitter-Schwarzschild space-time backround. To have an analytic head way we study in detail the two-dimensional case, assuming that the situation in four dimensions will not be much different conceptually. It is assumed, that quantum field is in a thermal state i.e. described by the planckian distribution for the exact modes in the geometry under consideration. We calculate approximately the expectation value of stress-energy tensor near the cosmological and black hole horizons. It is shown that for a generic temperature backreaction from quantum fields on the geometry cannot be neglected. Thus, de Sitter-Schwarzschild space-time geometry inevitably is strongly modified by the quantum fluctuations of the matter fields.