Unitarity of black hole evaporation in final-state projection models

TL;DR

This paper examines the final-state projection model of black hole evaporation, showing it can reconcile unitarity with smooth horizons and discussing implications for quantum mechanics and causality, with deviations being negligible for large black holes.

Contribution

It demonstrates that the final-state projection model can preserve unitarity and smooth horizons, even with generic boundary conditions, and explores the implications for causality and quantum mechanics.

Findings

Deviations from unitarity are exponentially small in black hole entropy.

The model allows cloning and polygamous entanglement, violating monogamy.

Causality violations are likely unobservable due to computational complexity.

Abstract

Almheiri et al. have emphasized that otherwise reasonable beliefs about black hole evaporation are incompatible with the monogamy of quantum entanglement, a general property of quantum mechanics. We investigate the final-state projection model of black hole evaporation proposed by Horowitz and Maldacena, pointing out that this model admits cloning of quantum states and polygamous entanglement, allowing unitarity of the evaporation process to be reconciled with smoothness of the black hole event horizon. Though the model seems to require carefully tuned dynamics to ensure exact unitarity of the black hole S-matrix, for a generic final-state boundary condition the deviations from unitarity are exponentially small in the black hole entropy; furthermore observers inside black holes need not detect any deviations from standard quantum mechanics. Though measurements performed inside old black holes could potentially produce causality-violating phenomena, the computational complexity of decoding the Hawking radiation may render the causality violation unobservable. Final-state projection models illustrate how inviolable principles of standard quantum mechanics might be circumvented in a theory of quantum gravity.