Black-hole evaporation in the Klein-Sauter-Heisenberg-Euler formalism

A generalization of the classical approach of barrier penetration introduced by Klein, Sauter, Heisenberg, and Euler to curved spaces endowed with future horizons is given. This technique allows one to recover most directly results obtained by Hawking recently. The treatment here presented encompasses, as special cases, the works of Deruelle and Ruffini, of Damour and Ruffini, and of Nakamura and Sato.