Internal Geometry of an Evaporating Black Hole

Abstract

We present a semiclassical model for the formation and evaporation of a four-dimensional black hole. We solve the equations numerically and obtain solutions describing the entire space-time geometry from the collapse to the end of the evaporation. The solutions satisfy the evaporation law $\dot{M}\propto {-M}^{-2\mathrm{}}$, which confirms dynamically that black holes do evaporate thermally. We find that the evaporation process is in fact the shrinking of a throat that connects a macroscopic interior "universe" to the asymptotically flat exterior. It ends either by pinching off the throat leaving a closed universe and a Minkowskian exterior or by freezing up when the throat's radius approaches a Planck size. In either case the macroscopic inner universe is the region where the information lost during the evaporation process is hidden.