Hawking radiation from an evaporating black hole via Bogoliubov transformations

Abstract We study Hawking radiation on a Vaidya space-time with gravitational collapse followed by evaporation. The collapsing body is null thin-shell and the evaporation induced negative energy null-shell. This mimics back-reaction to radiation. Using Hawking’s original method of Bogoliubov transformations we characterize radiated spectrum in near horizon approximation due spherically symmetric modes as dominated thermal emission an increasing effective temperature. compute this time dependent temperature find numerical agreement results obtained other techniques. known divergences at are explained divergent nature As consistency check, re-derived from zero mass limit remnant black hole scenario.