In terms of the Painleve-Gullstrand-Lemaitre coordinates a rather general s
cenario for the gravitational collapse of an object and the subsequent form
ation of a horizon is described by a manifest C-infinity metric. For a (1 1)-dimensional model of the collapse the leading contributions to the Bogo
liubov coefficients are calculated explicitly and the Hawking temperature i
s recovered. But depending on the particular dynamics of the collapse the f
inal stare represents either evaporation or antievaporation. The generaliza
tion of the calculation to 3 + 1 dimensions is outlined and possible implic
ations are addressed.