Evaporation of Charged Black Holes Near Extremality

Abstract

The quantum evolution of black holes including back reaction effects is an open problem. One can simplify it by considering the scattering of low-energy neutral particles off extremal Reissner-Nordström black holes [1]. If, in addition, we also consider spherically reduced configurations, the theory can be described, in a region very close to the horizon, by a solvable effective model. This model is just the Jackiw-Teitelboim model [2] (for details see [3])where the two-dimensional fields of (1) are related to the four-dimensional metric by the expression ds The above expression contains a cosmological term with λ 2 = l −2 q −3 to ensure that the extremal geometry remains an exact solution of the one-loop theory. The equations of motion derived from I + I P L in conformal gauge ds 2 = −e 2ρ dx + dx − are