A Brief History of Hawking's Information Paradox (European Physics Letters)

This is a short review of our recent work on black hole information for European Physics Letters.

A Brief History of Hawking's Information Paradox 

European Physics Letters 139 (2022) 49001

Xavier Calmet and Stephen D. H. Hsu 

Abstract 

In this invited review, we describe Hawking's information paradox and a recently proposed resolution of it. Explicit calculations demonstrate the existence of quantum hair on black holes, meaning that the quantum state of the external graviton field depends on the internal state of the black hole. Simple quantum mechanics then implies that Hawking radiation amplitudes depend on the internal state, resulting in a pure final radiation state that preserves unitarity and, importantly, violates a factorization assumption which is central to the original paradox. Black hole information is encoded in entangled macroscopic superposition states of the radiation. 

DOI: 10.1209/0295-5075/ac81e8

arXiv version: https://arxiv.org/abs/2207.08671

From Conclusions:

... The radiation amplitudes computed by Hawking, which describe thermal radiation emitted from a black hole at temperature T, already describe a broad distribution of possible radiation types, spins, and momenta emitted at each stage. Thus, even in the semiclassical approximation there are many distinct patterns of radiation in (6). The set of possible final states is already complex even at leading order, resulting in very different coarse grained patterns of energy-momentum density. Small corrections to the amplitudes α(E, r) due to quantum hair do not qualitatively change this situation, but they are necessary to unitarize the evaporation and they determine the precise relations between components of the entangled state. 

Importantly, no special assumptions about the amplitudes α(E, r) need to be made to determine that the factorized form of the state (2) does not hold. Factorization is assumed in essentially every formulation of the information paradox, but in reality is violated because the external graviton state depends on the internal black hole state. 

Known quantum gravitational effects leading to quantum hair are extremely small and thus difficult to probe experimentally or detect via observations. We cannot prove that our solution to the information paradox is unique. However, the consequences of quantum hair lead, without any speculative theoretical assumptions, to plausible unitary evaporation of black holes. The properties of quantum hair and the evaporation amplitude (6) can be deduced using only long wavelength properties of quantum gravity – they do not rely on assumptions about Planck scale physics or a specific short distance completion. Therefore, Occam’s razor favors quantum hair.