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The scattering matrix approach for the quantum black hole, an overview
General Relativity and Quantum Cosmology · Submitted 9 Jul 1996
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The approach is shown to be powerful in not only producing promising models for the quantum black hole, but also new insights concerning the dynamics of physical degrees of freedom in ordinary flat space-time.
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The abstract, sentence by sentence
If one assumes the validity of conventional quantum field theory in the vicinity of the horizon of a black hole, one does not find a quantum mechanical description of the entire black hole that even remotely resembles that of conventional forms of matter; in contrast with matter made out of ordinary particles one finds that, even if embedded in a finite volume, a black hole would be predicted to have a strictly continuous spectrum. Dissatisfied with such a result, which indeed hinges on assumptions concerning the horizon that may well be wrong, various investigators have now tried to formulate alternative approaches to the problem of ``quantizing" the black hole. We here review the approach based on the assumption of quantum mechanical purity and unitarity as a starting point, as has been advocated by the present author for some time, concentrating on the physics of the states that should live on a black hole horizon. The approach is shown to be powerful in not only producing promising models for the quantum black hole, but also new insights concerning the dynamics of physical degrees of freedom in ordinary flat space-time.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | If one assumes the validity of conventional quantum field theory in the vicinity of the horizon of a black hole, one does not find a quantum mechanical description of the entire black hole that even remotely resembles that of conventional forms of matter; in contrast with matter made out of ordinary particles one finds that, even if embedded in a finite volume, a black hole would be predicted to have a strictly continuous spectrum. | background 0.95 | 0.13 | 0.08 | asserted 0.94 |
| s1 | Dissatisfied with such a result, which indeed hinges on assumptions concerning the horizon that may well be wrong, various investigators have now tried to formulate alternative approaches to the problem of ``quantizing" the black hole. | background 0.86 | 0.05 | 0.04 | hedged possibility 0.81 |
| s2 | We here review the approach based on the assumption of quantum mechanical purity and unitarity as a starting point, as has been advocated by the present author for some time, concentrating on the physics of the states that should live on a black hole horizon. | contribution 0.76 | 0.41 | 0.14 | asserted 0.81 |
| s3 | The approach is shown to be powerful in not only producing promising models for the quantum black hole, but also new insights concerning the dynamics of physical degrees of freedom in ordinary flat space-time. | result 0.46 | 0.85 | 0.65 | asserted 0.99 |
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The paper
Original abstract
If one assumes the validity of conventional quantum field theory in the vicinity of the horizon of a black hole, one does not find a quantum mechanical description of the entire black hole that even remotely resembles that of conventional forms of matter; in contrast with matter made out of ordinary particles one finds that, even if embedded in a finite volume, a black hole would be predicted to have a strictly continuous spectrum. Dissatisfied with such a result, which indeed hinges on assumptions concerning the horizon that may well be wrong, various investigators have now tried to formulate alternative approaches to the problem of ``quantizing" the black hole. We here review the approach based on the assumption of quantum mechanical purity and unitarity as a starting point, as has been advocated by the present author for some time, concentrating on the physics of the states that should live on a black hole horizon. The approach is shown to be powerful in not only producing promising models for the quantum black hole, but also new insights concerning the dynamics of physical degrees of freedom in ordinary flat space-time.
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References
How later papers used it
75 later papers cite it
2 later papers by other authors are listed below: 1 built on it and 1 used its method or tool.
Builds on it 1 of 3 papers with this label
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Interpreted its complementary subalgebra as a generalization of this paper's gravitational shockwave algebra.
Quantization of Gravity on Null Hypersurfaces (2026) · 0.85 · paraphrased: the licence does not allow quoting
Uses its method or tool 1 of 3 papers with this label
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Followed this paper's formulation in its own work.
Calculation of Hawking Radiation in Local Field Theory (2021) · 1.00 · paraphrased: the licence does not allow quoting
How the literature uses it
67 arXiv papers cite this in 105 sentences
Papers citing it · 51 sentences without a confident label
Builds on it 2 papers
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Applying the arguments of 't Hooft at a black hole horizon [ref] to a light sheet horizon, it can be shown that these shifts obey uncertainty relations of the form Δδu(y) Δδv(y') = l^d-2_p f(y,y'),
Modular Fluctuations from Shockwave Geometries · Introduction · 0.90
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The complementary subalgebra 𝒜_□◯□ = π_(G_□^+ _◯ G_□^+) can be interpreted as a generalization of `t Hooft's gravitational shockwave algebra [ref] .
Quantization of Gravity on Null Hypersurfaces · Subcases · 0.85
Uses its method or tool 3 papers
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We basically follow 't Hooft's formulation [ref] in the following.
Calculation of Hawking Radiation in Local Field Theory · Rindler coordinate formulation due to 't Hooft · 1.00
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The density of states $N(E)$ is defined by [ref] [equation] where $r_+$ is the outer horizon, $h$ is the brick wall cutoff, $L$ is the IR cutoff and $m_max$ is the maximal value of the magnetic quantum number $m$ such that $P$ remains real and is given by [equation] In the lowest order in WKB we have [equation] where [equation] and the linear term in $a$ vanishes due to $∫_-m_max^m_max m dm=0$.
Noncommutative correction to the entropy of charged BTZ black hole · WKB and the density of states $N(E)$ · 0.87
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The brick-wall method, developed by 't Hooft [ref] provides an appropriate regularization using the WKB approximation and is compatible with the one-loop calculations [ref] .
Noncommutativity and logarithmic correction to the black hole entropy · Black hole entropy via the brick-wall model · 0.90
Compares with it 4 papers
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In fact, 't Hooft's uncertainty relations described in e.g. [ref] , when translated into a correlation function, are identical in form to our results, except in the normalization.
Observational Signatures of Quantum Gravity in Interferometers · Introduction · 1.00
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We also recall that in [ref] the shifts acquired by each shockwave as it crosses the other were promoted to non-commuting operators, while in [ref] we considered only one shockwave, but observed that the same commutation relations may be recovered if one identifies the shift of a would-be second shockwave with the background $C$.
An Infrared On-Shell Action and its Implications for Soft Charge Fluctuations in Asymptotically Flat Spacetimes · On-shell action = shockwave effective action · 0.96
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This is reminiscent of the brick-wall model [ref] (although the horizon may still remain uneventful for freely falling observers in our discussion).
Planckian Physics Comes Into Play At Planckian Distance From Horizon · Conclusion and discussion · 0.97
Cites it as background 35 papers
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In a complementary series of developments, 't Hooft proposed that incoming and outgoing modes near black hole horizons obey a set of commutation relations [ref] and used these to evaluate a universal contribution to the black hole S-matrix.
From Shockwaves to the Gravitational Memory Effect · Introduction · 0.97
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This amplitude has been investigated in detail over recent years [ref] .
Celestial Eikonal Amplitudes in the Near-Horizon Region · Introduction · 0.94
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Developed to study the effect of outgoing Hawking radiation on energetic particles traveling along the horizon of a black hole [ref] , the shockwave geometries have proved to provide insight where the quantum entanglement structure changes under the backreaction from infalling and outgoing matter, particularly in the context of black holes and the AdS/CFT correspondence [ref] .
Modular Fluctuations from Shockwave Geometries · Introduction · 0.95
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