LPTENS 96/10 TAU 2326-96 October 1996 THE SCHWINGER MECHANISM, THE UNRUH EFFECT AND THE PRODUCTION OF ACCELERATED BLACK HOLES

We compute the corrections to the transition amplitudes of an accelerated Unruh \box" that arise when the accelerated box is replaced by a \two level ion" immersed in a constant electric eld and treated in second quantization. There are two kinds of corrections, those due to recoil e ects induced by the momentum transfers and those due to pair creation. Taken together, these corrections show that there is a direct relationship between pair creation amplitudes described by the Heisenberg-Euler-Schwinger mechanism and the Unruh e ect, i.e. the thermalisation of accelerated systems at temperature a=2 where a is the acceleration. In particular, there is a thermodynamical consistency between both e ects whose origin is that the euclidean action governing pair creation rates acts as an entropy in delivering the Unruh temperature. Upon considering pair creation of charged black holes in an electric eld, these relationships explain why black holes are created from vacuum in thermal equilibrium, i.e. with their Hawking temperature equal to their Unruh temperature. Unit e propre de recherche du C.N.R.S. associee a l' Ecole Normale Sup erieure et a l'Universit e de Paris Sud.