VACUUM INSTABILITY AND BLACK-HOLE EVAPORATION

We pass in review the mechanisms of pair production in a static electric field and in black hole evaporation. New methods are developed in the electric case to show up the similarities with the black hole problem. The latter is then handled both through mode analysis and functional integration techniques wherein the situation of collapse is couched in terms of Eddington-Finkelstein coordinates. As in the electric case, the initial vacuum, identified with vacuum seen by a Schwarzschild observer before collapse, is unstable. We display in detail how it passes over to the Unruh vacuum. the quasi-stationary state which the Schwarzschild observer characterizes by the emitted thermal flux of Hawking.