PERTURBATIVE SOLUTION TO THE BACK REACTION PROBLEM FOR STATIC BLACK HOLES

Abstract

Using Israel’s description of static space-times with event horizons, we give a general (2+2) formulation of semiclassical Einstein equations in four dimensions in terms of two-dimensional quantities. We find analytic expressions for the metric coefficients in the spherically symmetric case and in a perturbative scheme (taking Schwarzschild’s metric as a zero order solution and the perturbation parameters Mpl/M, Mpl and M being the planck and black hole masses respectively). Modifications to the horizon radius, Hawking temperature, luminosity and lifetime of evaporating black holes are found due to the back reaction. Two different situations appear depending on the graviton-matter balance. If matter is relevant, the temperature is increased and thus the lifetime decreased from their standard values TH=1/8πM and τH=CM3. If graviton is dominant T is smaller than TH and, more important, it can have a maximum at M~Mpl and then go to zero. The connection with string theory is discussed.