Back reaction of Hawking radiation on black hole geometry

We propose a model for the geometry of a dynamical spherical shell in which the metric is asymptotically Schwarzschild, but deviates from Ricci flatness in a finite neighborhood of the shell. Hence, the geometry corresponds to a “hairy” black hole, with the hair originating on the shell. The metric is regular for an infalling shell, but it bifurcates, leading to two disconnected Schwarzschild-like spacetime geometries. The shell is interpreted as either collapsing matter or as Hawking radiation, depending on whether or not the shell is infalling or outgoing. In this model, the Hawking radiation results from tunneling between the two geometries. Using this model, the back reaction correction from Hawking radiation is calculated.