A Quantum Superposition of Black Hole Evaporation Histories: Recovering Unitarity

TL;DR

This paper introduces a quantum model of black hole evaporation where the black hole exists in a superposition of states, demonstrating that unitarity can be preserved and information recovered, addressing the black hole information paradox.

Contribution

It presents a toy quantum model allowing superpositions of black hole states and proves that such a model can be unitary, preserving information during evaporation.

Findings

Black hole can be in a superposition of evaporated and non-evaporated states.

The model shows the probability of full evaporation approaches certainty over time.

Unitarity is maintained, enabling potential information recovery from Hawking radiation.

Abstract

Black hole evaporation is one of the most striking phenomena at the interface between gravity and quantum physics. In Hawking's semi-classical treatment, where matter is quantum mechanical and the spacetime is definite and classical, evaporation leads to an apparent loss of unitarity of the overall evolution, and to the so-called black hole information paradox. Here, we go beyond this semi-classical treatment and formulate a toy quantum model of black hole evaporation that allows the black hole to evolve into a superposition of being fully evaporated and not fully evaporated, consistent with the Hawking particles being in a coherent superposition of different energy levels. We model Hawking particle production by the repeated action of quantum-controlled unitaries, generating emission from the quantum black hole and accounting for a quantum coherent back-reaction on the black hole matter state. We show that the probability of full annihilation of the black hole matter increases with time until the black hole is, asymptotically, fully evaporated in every branch of the quantum superposition. We prove that under natural assumptions, this evaporation model is unitary, such that the initial state can in principle be recovered from the final asymptotic state of the radiation.