Quantum Hair from Gravity (published version in Physical Review Letters)

This is the published version of our paper on Quantum Hair on black holes, in Physical Review Letters:

Quantum Hair from Gravity 

Xavier Calmet, Roberto Casadio, Stephen D. H. Hsu, and Folkert Kuipers 

Phys. Rev. Lett. 128, 111301 – Published 17 March 2022 

We explore the relationship between the quantum state of a compact matter source and of its asymptotic graviton field. For a matter source in an energy eigenstate, the graviton state is determined at leading order by the energy eigenvalue. Insofar as there are no accidental energy degeneracies there is a one to one map between graviton states on the boundary of spacetime and the matter source states. Effective field theory allows us to compute a purely quantum gravitational effect which causes the subleading asymptotic behavior of the graviton state to depend on the internal structure of the source. This establishes the existence of ubiquitous quantum hair due to gravitational effects.

The paper establishes that the quantum state of the graviton field (equivalently, the spacetime metric) of a compact matter source depends on the quantum state of the source. This can be established without a short distance theory of quantum gravity -- i.e., near the Planck length. Our results are long wavelength effects and are insensitive to the details of short distance physics, such as whether gravitons are excitations of strings, or something else, at the most fundamental level.

Classical theorems in General Relativity indicate that black holes are nearly featureless -- only a few aspects of the hole, such as its total mass, charge, and angular momentum, are manifested in its asymptotic gravitational field. We show that this "no hair" property does not extend to the quantum realm. Indeed at the quantum level the situation is the opposite: the full quantum state of the compact object can be recovered from the asymptotic graviton state.

In this companion paper we show how these results resolve Hawking's black hole information paradox, which has been an open problem for 46 years.

Quantum hair and black hole information 

Physics Letters B Volume 827, 10 April 2022, 136995 

Xavier Calmet and Stephen D.H. Hsu 

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.

Note to experts: the companion paper explains why Mathur's Theorem (i.e., entanglement entropy must always increase by ~ln 2 with each emitted qubit) is evaded once one considers BH evolution in the full radiation Hilbert space. The radiation Hilbert space is much larger than the small subspace which remains after conditioning on any specific spacetime background or BH recoil trajectory. Even exponentially small entanglement between different radiation states (mediated by quantum hair) can unitarize the evaporation process.

This is also explained in detail in the talk video and slides linked below.

Press coverage:

BBC

Guardian

Independent

Earlier discussion, with more background on the Hawking paradox. See especially the important work by Suvrat Raju and collaborators: 

Quantum Hair and Black Hole Information (December 2021) 

Has Hawking's Black Hole Information Paradox Been Resolved? (November 2021)

Video of seminar and slides.