Quantum mechanics of a black hole
Open accessAbstract
Beginning with Bekenstein, many authors have considered a uniformly spaced discrete quantum spectrum for the black hole horizon area. It is also believed that the huge degeneracy of these area levels corresponds to the notion of black hole entropy. Starting from these two assumptions we here infer the algebra of a Schwarzschild black hole's observables. This algebra then serves as motivation for introducing in the system's Hamiltonian an interaction term. The interaction contains the horizon area operator, which is a number operator, and its canonical conjugate, the phase operator. The Hawking radiation from a Schwarzschild black hole is seen to be a consequence of an area-phase interaction. Using this interaction we have reproduced the semiclassical result for the Hawking radiation power. Furthermore, we show that the initial state of the black hole determines the nature of its development. Thus, a state which is an area eigenstate describes a static eternal black hole, but a coherent state describes a radiating black hole. Hence, it is the observer's initial knowledge or uncertainty about the horizon area which determines the evolution.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The spectroscopy for spherically symmetric black holes is unaltered by the area spectrum (42) because it becomes uniformly spaced for large j, like spectrum (36).
“As a last remark we note that the spectroscopy for spherically symmetric black holes (cf, e.g., [46]) is unaltered by our area spectrum (42) because it becomes uniformly spaced for large j , like the spectrum (36).”
From Symmetry reduction for quantized diffeomorphism-invariant theories of connections (2000) · cites this paper as [46]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Particle creation by black holes
Hawking, S. W. (1975) · Communications In Mathematical Physics · doi:10.1007/bf02345020 · Cited by 13,106 · see citing works
Bekenstein, J. D. (1973) · Physical Review D · doi:10.1103/physrevd.7.2333 · Cited by 7,555 · see citing works
HAWKING, S. W. (1974) · Nature · doi:10.1038/248030a0 · Cited by 5,669 · see citing works
Sakurai, J. J., & Napolitano, J. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108587280 · Cited by 3,672 · see citing works
General Relativity – An Einstein Centenary Survey
Irvine, J. M. (1980) · Physics Bulletin · doi:10.1088/0031-9112/31/4/029 · Cited by 2,871 · see citing works
Breakdown of predictability in gravitational collapse
Hawking, S. W. (1976) · Physical Review D · doi:10.1103/physrevd.14.2460 · Cited by 2,554 · see citing works
Polchinski, J. (1998) · Cambridge University Press eBooks · doi:10.1017/cbo9780511618123 · Cited by 1,663 · see citing works
(1979) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1,590 · see citing works
Bussey, P. J. (2021) · Contemporary Physics · doi:10.1080/00107514.2021.1924275 · Cited by 1,436 · see citing works
Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole
Page, D. N. (1976) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.13.198 · Cited by 1,316 · see citing works
Gravitational Radiation from Colliding Black Holes
Hawking, S. W. (1971) · Physical Review Letters · doi:10.1103/physrevlett.26.1344 · Cited by 1,142 · see citing works
Charap, J. M. (1985) · Contemporary Physics · doi:10.1080/00107518508210746 · Cited by 765 · see citing works
Bohr's Correspondence Principle and the Area Spectrum of Quantum Black Holes
Hod, S. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.4293 · Cited by 729 · see citing works
Reversible and Irreversible Transformations in Black-Hole Physics
Christodoulou, D. (1970) · Physical Review Letters · doi:10.1103/physrevlett.25.1596 · Cited by 705 · see citing works
RUFFINI, R. J., & WHEELER, J. A. (1971) · Physics Today · doi:10.1063/1.3022513 · Cited by 670 · see citing works
The quantum mass spectrum of the Kerr black hole
Bekenstein, J. D. (1974) · Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento · doi:10.1007/bf02762768 · Cited by 584 · see citing works
Spectroscopy of the quantum black hole
Bekenstein, J. D., & Mukhanov, V. F. (1995) · Physics Letters B · doi:10.1016/0370-2693(95)01148-j · Cited by 432 · see citing works
Weaving a classical metric with quantum threads
Ashtekar, A., Rovelli, C., & Smolin, L. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.237 · Cited by 399 · see citing works
The quantum phase problem: a critical review
Lynch, R. (1995) · Physics Reports · doi:10.1016/0370-1573(94)00095-k · Cited by 303 · see citing works
Area spectrum of the Schwarzschild black hole
Louko, J., & Mäkelä, J. (1996) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.54.4982 · Cited by 148 · see citing works
Carlip, S., & Teitelboim, C. (1995) · Classical and Quantum Gravity · doi:10.1088/0264-9381/12/7/011 · Cited by 137 · see citing works
Black Holes, Gravitational Radiation and the Universe
Iyer, B. R., & Bhawal, B. (1999) · Springer eBooks · doi:10.1007/978-94-017-0934-7 · Cited by 134 · see citing works
The quantum levels of isolated spherically symmetric gravitational systems
Kastrup, H. A. (1996) · Physics Letters B · doi:10.1016/0370-2693(96)00846-5 · Cited by 101 · see citing works
Canonical quantum statistics of an isolated Schwarzschild black hole with a spectrum
Kastrup, H. A. (1997) · Physics Letters B · doi:10.1016/s0370-2693(97)01121-0 · Cited by 80 · see citing works
Hod, S. (1998) · Physical Review D · doi:10.1103/physrevd.59.024014 · Cited by 70 · see citing works
Fluctuations of the Hawking flux
Wu, C.-H., & Ford, L. H. (1999) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.60.104013 · Cited by 66 · see citing works
Phase volume occupied by a test particle around an incipient black hole
Padmanabhan, Τ. (1989) · Physics Letters A · doi:10.1016/0375-9601(89)90562-8 · Cited by 37 · see citing works
On the spectrum of the radiation from a naked singularity
Vaz, C., & Witten, L. (1998) · Physics Letters B · doi:10.1016/s0370-2693(98)01221-0 · Cited by 35 · see citing works
Schwarzschild black hole as a grand canonical ensemble
Gour, G. (1999) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.61.021501 · Cited by 31 · see citing works
Self-citationEvidence for the adiabatic invariance of the black hole horizon area
Mayo, A. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.58.104007 · Cited by 24 · see citing works
Flagged first, then by citations
Research works printed but not linked: 4
- [4]A. Ashtekar and K. Krasnov, gr-qc/9804039; A. Ashtekar, C. Rovelli and L. Smolin, Phys. Rev. Letters 69 , 237 (1992). · arXiv
- [6]V. Mukhanov, Pis. Eksp. Teor. Fiz. 44 , 50 (1986) [JETP Letters 44 , 63 (1986)]
- [15]M. Born, Atomic Physics (Blackie, London 1969), eight edition.
- [35]H. Umezawa, Advanced Field Theory (AIP Press, New York, 1995).
Cited by
Sorted by citations
Symmetry reduction for quantized diffeomorphism-invariant theories of connections
Bojowald, M., & Kastrup, H. A. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/15/311 · Cited by 168 · see citing works
- Authors
- Gour, G.
- Affiliations
- Hebrew University of Jerusalem (IL)
- Corresponding author
- Gour, Gilad
- ORCID
- Gour, Gilad
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2000-05-15
- Volume
- 61
- Issue
- 12
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2049254165
- Cited by
- 20
- References
- 30
- Citations by year
- 2014: 1
- FWCI
- 2.23
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Keywords
- black hole quantum mechanics, Schwarzschild black hole, black hole entropy, Hawking radiation, area operator, phase operator, coherent states, black hole evolution
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
