A brief history of Hawking's information paradox

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 quantummechanics 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.

Quantum gravitational corrections to particle creation by black holes

“…In order to perform explicit calculations we considered quantum hair which manifests as a semiclassical correction to the exterior metric. In general, as discussed in [6][7][8], the quantum state of the black hole interior is reflected in the quantum state Ψ g of its exterior graviton field. Ψ g will affect radiation amplitudes: i.e., it represents the background or environment in which the Hawking radiation originates.…”

“…In a series of recent papers [2][3][4][5][6][7][8][9], it has been shown that quantum gravitational corrections generically lead to quantum hair. In other words, classical solutions to Einstein's equations generically receive quantum gravitational corrections.…”

Nonthermal radiation of evaporating black holes

“…where Ω > 0 is a parameter, and θ is the Heaviside step function. Rindler modes φ 1Ω and φ 2Ω are solutions of the wave equation (7), and for Ω > 0 have positive norm (defined as the Klein-Gordon inner product). The mode functions (8) and ( 9) are non-zero outside and inside the BH event horizon (line T = X) respectively (see Fig.…”

“…This is known as the BH information paradox [5]. For proposals to resolve the BH information problem see, e.g., [6,7] and references therein.…”

Generalized Unruh effect: A potential resolution to the black hole information paradox

“…One of the highly intriguing interpretations of the generalized Unruh effect is its application to the 'Black Hole Information Paradox' [22][23][24]. By scrutinizing the evolution of plane wave modes inside the shell of a collapsing shell metric, we found a non-trivial mapping between arbitrary density matrix generated by the in-shell plane wave Fock states and the pseudo-thermal density matrix generated by the positive frequency modes living at the asymptotically flat region outside the Schwarzschild black hole horizon.…”