On Radiative Fluxes and Coulombic Charges in the Balance Law for Black Hole Evaporation

For classical massless fields in 3+1 dimensions, there is a clear distinction between Coulombic charges and radiative fluxes, and their relation is encoded in flux-balance laws. We extend the analysis of these classical flux-balance laws in general relativity to semiclassical gravity, and investigate its consequences for backreaction in black hole evaporation. In a spherically symmetric model, we show that the standard Davies-Fulling formula for the energy flux F decomposes into a radiative and a Coulombic piece, F = F_rad+ F_Coul. The Coulombic contribution is identified as the derivative of a gravitational charge which renormalizes the black hole mass, resulting in a physical flux-balance law. We discuss the relation of this result to the Ashtekar-Taveras-Varadarajan proposal for CGHS black holes, and illustrate its implications for black hole evaporation in 3+1 dimensions.