A Possible Resolution of the Black Hole Information Puzzle

TL;DR

It is argued that the decay rate in the black hole rest frame is necessarily proportional to $e^{-S_{tot}}$, where $S_tot$ is the total entropy produced during the evaporation process, entailing a very long-lived remnant.

Abstract

The problem of information loss is considered under the assumption that the process of black hole evaporation terminates in the decay of the black hole interior into a baby universe. We show that such theories can be decomposed into superselection sectors labeled by eigenvalues of the third-quantized baby universe field operator, and that scattering is unitary within each superselection sector. This result relies crucially on the quantum-mechanical variability of the decay time. It is further argued that the decay rate in the black hole rest frame is necessarily proportional to $e^{-S_{tot}}$, where $S_{tot}$ is the total entropy produced during the evaporation process, entailing a very long-lived remnant.

Figures (3)

• Figure 1: A large infalling matter pulse forms a black hole (shaded region) which evaporates down to zero size at the endpoint. Shortly thereafter, the black hole interior splits off from the exterior spacetime. The exterior spacetime settles back to the vacuum, and the Bondi mass accordingly vanishes at $i^+$. $\tau$ measures the proper time after the endpoint along the worldline indicated.
• Figure 2: In Hawkings proposal, a $\$$-matrix is formed by tracing over everything which falls in to the black hole. This trace effectively sews together the left and right portions (representing $S$ and $S^\dagger$) of each diagram. Contributions to $\$$ arising from one or two black holes are depicted.
• Figure 3: Third quantization implies that the baby universes are distinguishable only by their internal state, and not by the spacetime location of the black hole from which they were created. One accordingly must sew the left and right halves of the diagrams together in all possible ways. This has no consequence for the one-black-hole sector of $\$$, but for two black holes, there is one extra diagram, as illustrated.