Compare · Black Holes

Hawking's Information Loss vs Soft Hair

Black Hole Information Paradox · within family

	Hawking's Information Loss Historical	Soft Hair Frontier
Proposed	1976	2016
Key figures	Stephen Hawking	Stephen Hawking, Malcolm Perry, Andrew Strominger
In one sentence	Hawking argued in 1976 that an evaporating black hole destroys the information about what fell in, which limits prediction beyond ordinary quantum uncertainty.	The no-hair theorem says a classical black hole is characterized by only mass, charge, and angular momentum. Hawking, Perry, and Strominger argued in 2016 that this is technically incomplete: black holes also carry infinitely many conserved 'soft' charges, very-low-energy quantum excitations sitting at the horizon. Information about what fell in is stored in this soft hair.
Predictions	A black hole that forms and then evaporates completely turns a pure quantum state into a mixed one, so [[unitarity]] fails for the process as a whole The outgoing radiation carries no record of what fell in beyond the black hole's mass, angular momentum and charge No S-matrix exists for black hole formation and evaporation. A superscattering operator, which maps density matrices to density matrices, takes its place The entropy of the radiation never turns back down as the black hole shrinks, so the radiation does not follow the [[Page curve]] Gravitational collapse sets a limit on prediction that is fundamental and comes on top of quantum uncertainty	Black holes carry infinitely many faint quantum imprints, the soft charges, tied to subtle gravitational symmetries at infinity (BMS supertranslations and superrotations); these can in principle be detected as tiny patterns in the gravitational field measured by detectors very far away Two black holes with the same mass, charge, and angular momentum but different histories of what fell in differ in their soft-hair spectra; the difference is recoverable from sufficiently sensitive asymptotic measurements Hawking radiation carries correlations matching the soft-charge spectrum of the emitting black hole; in principle measurable, in practice astronomically far from current detector capabilities Memory effects in gravitational waves (permanent strain in distant detectors after a passing wave) are imprints of the same BMS structure that underpins soft hair, and have been observationally targeted by LIGO
Where it breaks	Banks, Susskind and Peskin argued in 1984 that any evolution law of this kind violates either locality or energy-momentum conservation Page estimated in 1993 that information may leak out so slowly at first that a calculation expanded in the ratio of Planck mass to black hole mass would miss it Hawking argued in 2005 that information is preserved, using a Euclidean path-integral argument restricted to asymptotically anti-de Sitter spacetimes. It was not a microscopic account of how the information gets out Penington derived the Page curve in 2019 within a semiclassical gravity calculation for an evaporating black hole in [[anti-de Sitter space]]. It shows how information can escape in that framework; it is a calculation, not an observation	The original 2016 paper sketched an information-encoding mechanism but did not demonstrate that the soft modes actually carry enough information to encode arbitrary matter falling into the black hole; the counting argument was incomplete Several follow-up papers (Bousso-Porrati 2017 among others) argued that the soft-hair charges are pure gauge in a precise sense and therefore cannot carry the information they were proposed to carry; this critique is contested but unresolved Soft hair does not connect cleanly to the replica-wormhole / entanglement-wedge picture that has dominated the post-2019 literature; the two approaches are not known to be reconcilable or to be incompatible Most of the technical development of soft modes since 2016 has happened in the celestial-CFT and asymptotic-symmetry program, somewhat separately from the information-paradox debate proper
Key unresolved problem	The locality problem: no one has written down an evolution law for information loss that keeps both locality and energy conservation, the obstacle Banks, Susskind and Peskin raised in 1984.	The not-enough-storage problem: no one has shown that soft charges, faint imprints matter leaves at the horizon, can actually hold all the detail of whatever fell in, so the central storage claim is undemonstrated.
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Hawking's Information Loss

1976 · Historical

Soft Hair

2016 · Frontier

Proposed

1976

2016

Key figures

Stephen Hawking

Stephen Hawking, Malcolm Perry, Andrew Strominger

In one sentence

Hawking argued in 1976 that an evaporating black hole destroys the information about what fell in, which limits prediction beyond ordinary quantum uncertainty.

The no-hair theorem says a classical black hole is characterized by only mass, charge, and angular momentum. Hawking, Perry, and Strominger argued in 2016 that this is technically incomplete: black holes also carry infinitely many conserved 'soft' charges, very-low-energy quantum excitations sitting at the horizon. Information about what fell in is stored in this soft hair.

Predictions

A black hole that forms and then evaporates completely turns a pure quantum state into a mixed one, so [[unitarity]] fails for the process as a whole
The outgoing radiation carries no record of what fell in beyond the black hole's mass, angular momentum and charge
No S-matrix exists for black hole formation and evaporation. A superscattering operator, which maps density matrices to density matrices, takes its place
The entropy of the radiation never turns back down as the black hole shrinks, so the radiation does not follow the [[Page curve]]
Gravitational collapse sets a limit on prediction that is fundamental and comes on top of quantum uncertainty

Black holes carry infinitely many faint quantum imprints, the soft charges, tied to subtle gravitational symmetries at infinity (BMS supertranslations and superrotations); these can in principle be detected as tiny patterns in the gravitational field measured by detectors very far away
Two black holes with the same mass, charge, and angular momentum but different histories of what fell in differ in their soft-hair spectra; the difference is recoverable from sufficiently sensitive asymptotic measurements
Hawking radiation carries correlations matching the soft-charge spectrum of the emitting black hole; in principle measurable, in practice astronomically far from current detector capabilities
Memory effects in gravitational waves (permanent strain in distant detectors after a passing wave) are imprints of the same BMS structure that underpins soft hair, and have been observationally targeted by LIGO

Where it breaks

Banks, Susskind and Peskin argued in 1984 that any evolution law of this kind violates either locality or energy-momentum conservation
Page estimated in 1993 that information may leak out so slowly at first that a calculation expanded in the ratio of Planck mass to black hole mass would miss it
Hawking argued in 2005 that information is preserved, using a Euclidean path-integral argument restricted to asymptotically anti-de Sitter spacetimes. It was not a microscopic account of how the information gets out
Penington derived the Page curve in 2019 within a semiclassical gravity calculation for an evaporating black hole in [[anti-de Sitter space]]. It shows how information can escape in that framework; it is a calculation, not an observation

The original 2016 paper sketched an information-encoding mechanism but did not demonstrate that the soft modes actually carry enough information to encode arbitrary matter falling into the black hole; the counting argument was incomplete
Several follow-up papers (Bousso-Porrati 2017 among others) argued that the soft-hair charges are pure gauge in a precise sense and therefore cannot carry the information they were proposed to carry; this critique is contested but unresolved
Soft hair does not connect cleanly to the replica-wormhole / entanglement-wedge picture that has dominated the post-2019 literature; the two approaches are not known to be reconcilable or to be incompatible
Most of the technical development of soft modes since 2016 has happened in the celestial-CFT and asymptotic-symmetry program, somewhat separately from the information-paradox debate proper

Key unresolved problem

The locality problem: no one has written down an evolution law for information loss that keeps both locality and energy conservation, the obstacle Banks, Susskind and Peskin raised in 1984.

The not-enough-storage problem: no one has shown that soft charges, faint imprints matter leaves at the horizon, can actually hold all the detail of whatever fell in, so the central storage claim is undemonstrated.

Reader vote

No votes yet