Quantum Hair and Black Hole Information (Physics Letters B published version)

This is the published version of our recent arxiv preprint, previously discussed here.

Quantum hair and black hole information 

https://doi.org/10.1016/j.physletb.2022.136995 

Abstract 

It has been shown that the quantum state of the graviton field outside a black hole horizon carries information about the internal state of the hole. We explain how this allows unitary evaporation: the final radiation state is a complex superposition which depends linearly on the initial black hole state. Under time reversal, the radiation state evolves back to the original black hole quantum state. Formulations of the information paradox on a fixed semiclassical geometry describe only a small subset of the evaporation Hilbert space, and do not exclude overall unitarity.

The earlier paper, which established the existence of quantum hair, has been accepted by PRL and should also appear soon. 

Seminar video and slides. 

From the paper:

4. Conclusion 

Hawking's information paradox has been the focus of intense interest for almost 50 years. In his 1992 lecture on the subject, John Preskill wrote [5] 

I conclude that the information loss paradox may well presage a revolution in fundamental physics. 

The resolution described here is conservative: the quantum state of the exterior gravity field is determined by the interior black hole state, allowing the latter to influence Hawking radiation produced at the horizon. Two distinct quantum states of the black hole may produce the same semiclassical external geometry, but the graviton states differ at the quantum level. The relationship between interior and exterior quantum states is not governed by classical no-hair theorems. Indeed, it has gradually been appreciated that gravity itself prevents the localization of quantum information [4], [9], [10], [11], [21], [22], [23], even behind a horizon. We stress that all formulations of the paradox require a degree of factorization between the black hole internal state and the radiation (see, e.g., (6)), which is clearly not true of our equation (4). 

Certain aspects of our expressions (2)-(4) are very clear: the black hole information is spread over many branches of the final radiation state, and macroscopic superpositions of different spacetime geometries play a role in the evaporation. Some of the difficulty in resolving the paradox may originate from a reluctance to accept these aspects of quantum dynamics.