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Don N. Page | Physical Review Letters | (1993)
Primary Link Pubmed DOI Openalex Full text (OA)

Abstract

If black hole formation and evaporation can be described by an S matrix, information would be expected to come out in black hole radiation. An estimate shows that it may come out initially so slowly, or else be so spread out, that it would never show up in an analysis perturbative in MPlanck/M, or in 1/N for two-dimensional dilatonic black holes with a large number N of minimally coupled scalar fields. Alberta-Thy-24-93, hep-th/9306083. 1 Hawking’s calculation of thermal emission from a stationary classical black hole [1, 2] soon led to a major unresolved puzzle concerning quantum mechanics and gravity: what happens to a pure quantum state that collapses to form a black hole which emits approximately themal radiation? Hawking proposed [2] that the black hole would eventually disappear completely and that the resulting state of radiation, like a precisely thermal state, would be mixed. In other words, information would be permanently lost down the black hole, and there would be no S matrix to take an initial pure state to a final pure state. It was soon objected [3, 4] that this conclusion is not justified by the classical or semiclassical approximation for the black hole used to derive it, and that, in its original form at least, it violates a strong form of CPT invariance [4]. A number of alternative possibilities were given [4]. The main options now under active investigation seem to be that either most of the information comes out with the bulk of the radiation to give an S matrix [4, 5, 6, 7], or most of the information goes into a long-lived [8, 9] or absolutely stable remnant [10], or else information is lost from our universe as Hawking proposed [2]. For recent reviews of the problem, see

Tags

Sample Definition And Size

The paper is a theoretical analysis and does not involve empirical subjects or sample sizes. It considers a model of black hole formation and evaporation, including two-dimensional dilatonic black holes with a large number N of minimally coupled scalar fields, but does not specify a numerical sample size beyond this theoretical framework.

Study Type

The work is a theoretical physics paper, specifically a conceptual and analytical study in quantum gravity and black hole thermodynamics, published as a journal article in Physical Review Letters.

Conflicts Of Interest

No conflicts of interest are declared in the publication; standard for theoretical physics papers of this type, and none are indicated in the metadata or abstract.

Results Summary

The key finding is that if black hole formation and evaporation can be described by an S‑matrix, information would be expected to emerge in the radiation. However, the estimate shows that this information may emerge so slowly or be so diffusely distributed that it would not appear in perturbative analyses in M_Planck/M or in 1/N expansions for two‑dimensional dilatonic black holes with large N of minimally coupled scalar fields.

Referenced In

StarTalk

Season 17, Episode 6: The Black Hole Information Paradox Explained

Hey StarTalkians! In Season 17, Episode 6, Neil and Chuck tackle another collection of Cosmic Queries, with a focus on black holes. One question they received touched the black hole information paradox. 

Incoming Asteroids, Moving Black Holes, & More! | Cosmic Queries #104

The Queries episodes are great for covering a lot of ground, but it’s easy to get a little lost during the brief explanations. Neil covered the main points broadly, but here’s a more detailed explanation.

Hawking Radiation and Information in a Black Hole

Stephen Hawking made a huge stir in the 1970s with his research on how quantum mechanics works on the edge of a black hole (Breakdown of predictability in gravitational collapse).

The basic idea depends on pair production. It’s like the universe has an energy bank account and after a quick loan, a pair of one particle and one anti-particle can emerge. But that loan has to be paid back: they combine, annihilate and the energy debt is repaid.

Hawking wondered, what happens if this happens on the very edge of a black hole? One particle might fall in while the other escapes into space.

If this happens, who pays the energy debt? The black hole. He concluded that black holes must evaporate by emitting radiation – called Hawking radiation – to repay this debt.

The problem is that you can’t get the original particle’s information from the radiation that comes out. It’s like trying to reconstruct an ancient stone by studying the grains of sand on the beach.

But if the information is lost, it’s not possible to determine what happened in the past by studying the present. It throws the whole project of physics into question.

The Black Hole Information Paradox

Hawking’s student, Don Page, came back in the 1990s with an ingenious insight (Information in black hole radiation). He realized that the radiation would carry information from the black hole via quantum entanglement.

Page showed that the “entanglement entropy” – the information contained in the entangled state – would increase as the black hole evaporated, but would decline back to zero as the black hole disappears.

The only problem is that nobody knew how the entropy trend could just reverse like this. Physicists were left with a paradox: either weird new physics was needed way sooner than expected, or Hawking was right and information is lost forever.

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