  We present a proof of the existence of the Hawking radiation for massive
bosons in the Schwarzchild-de Sitter metric. It provides estimates for the
rates of decay of the initial quantum state to the Hawking thermal state. The
arguments in the proof include a construction of radiation fields by conformal
scattering theory; a semiclassical interpretation of the blueshift effect; and
the use of a WKB parametrix near the surface of a collapsing star. The proof
does not rely on the spherical symmetry of the spacetime.
