Quantum field theory in curved spacetime
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It is universally agreed that independently the theory of general relativity and quantum field theory are very successful theories. When static black holes are considered, it seems natural, that quantum field effects should have an impact on it without invoking quantum gravitational effects due to the scale of the problem. The general result is that the black hole, which was though to be static, is actually evaporating by slowly emitting particles with charge, angular momentum and energy. In this paper we consider transition of scalar field transition through a collapsing shell of matter, which latter forms a static spherically symmetric black hole. Analysis includes the use of Heun functions, which generalize hypergeometric functions.