The Internal Geometry of an Evaporating Black Hole

TL;DR

This paper models the entire process of black hole formation and evaporation using a semi-classical approach, revealing the shrinking of a throat that connects an interior universe to the exterior, and discussing the fate of information.

Contribution

It provides a numerical semi-classical model of black hole evaporation, illustrating the dynamic geometry and potential end states of the process.

Findings

Evaporation follows the law: $ ext{d}M/ ext{d}t \,\propto -M^{-2}$.

The evaporation process involves the shrinking of a throat connecting interior and exterior.

The interior region potentially retains the information lost during evaporation.

Abstract

We present a semi-classical model for the formation and evaporation of a four dimensional black hole. We solve the equations numerically and obtain solutions describing the entire the space-time geometry from the collapse to the end of the evaporation. The solutions satisfy the evaporation law: $\dot M \propto -M^{-2}$ 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.