CoChat
Sign Up
Cited by 580Black Holes and Theoretical PhysicsNoncommutative and Quantum Gravity TheoriesRelativity and Gravitational Theory

Quantum geometry of isolated horizons and black hole entropy

Open access
Ashtekar, Abhay, Baez, John C., Krasnov, Kirill·2000·Advances in Theoretical and Mathematical Physics
DOI 10.4310/atmp.2000.v4.n1.a1
Open this paper in CoChat — free accountOpen PDF

Abstract

Using the classical Hamiltonian framework of [1] as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting non-rotating isolated horizons as inner boundaries.The emphasis is on the quantum geometry of the horizon.Polymer excitations of the bulk quantum geometry pierce the horizon endowing it with area.The intrinsic geometry of the horizon is then described by the quantum Chern-Simons theory of a U(l) connection on a punctured 2-sphere, the horizon.Subtle mathematical features of the quantum Chern-Simons theory turn out to be important for the existence of a coherent quantum theory of the horizon geometry.Heuristically, the intrinsic geometry is flat everywhere except at the punctures.The distributional curvature of the U(l) connection at the punctures gives rise to quantized deficit angles which account for the overall curvature.For macroscopic black holes, the logarithm of the number of these horizon microstates is proportional to the area, irrespective of the values of (non-gravitational) charges.Thus, the black hole entropy can be accounted for entirely by the quantum states of the horizon geometry.Our analysis is applicable to all nonrotating black holes, including the astrophysically interesting ones which are very far from extremality.Furthermore, cosmological horizons (to which statistical mechanical considerations are known to apply) are naturally incorporated.An effort has been made to make the paper self-contained by including short reviews of the background material.

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.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.4310/atmp.2000.v4.n1.a1

Cites

77 of 77 references verified0 citation errors · 0 not checkable

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.

A few free checks a day · papers already verified open instantly · results are public

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

Flagged first, then by citations

Research works printed but not linked: 11

  1. [9]9. Ashtekar, C. Beetle, O. Dreyer, S. Fairhurst, B. Krishnan, J. Lewandowski, and J. Wisniewski, Generic isolated horizons and their applications, Phys. Rev. Lett, (in press);
  2. [10]10. C. Beetle, Isolated horizons and black hole mechanics, Penn State Ph.D. Dissertation.
  3. [14]14. K. Krasnov, On statistical mechanics of Schwarzschild black holes, Gen. Rel. Grav., 30 (1998), 53-68.
  4. [18]18. A. Ashtekar and C.J. Isham, Representation of the holonomy al- gebras of gravity and non-Abelian gauge theories, Class. Quant. Grav., 9 (1992), 1433-1467.
  5. [19]19. A. Ashtekar and J. Lewandowski, Representation theory of analytic holonomy algebras, in 'Knots and Quantum Gravity', edited by J.C. Baez, Oxford U. Press, Oxford, 1994.
  6. [21]21. A. Ashtekar and J. Lewandowski, Projective techniques and func- tional integration, Jour. Math. Phys., 36 (1995), 2170-2191.
  7. [24]24. R. Penrose, Angular momentum: an approach to combinatorial space-time, in 'Quantum Theory and Beyond', edited by Ted Bastin, Cambridge University Press, 1971.
  8. [42]42. T. Thiemann, Quantum spin dynamics, Class. Quant. Grav., 15 (1998), 839-873.
  9. [45]45. I.E. Segal, The complex-wave representation of the free boson field, in 'Topics in Functional Analysis', edited by I. Gohberg and M. Kac, Adv. Math. Suppl. Studies, Vol. 3, Academic Press, New York, (1978), 321-343.
  10. [53]53. A. Ashtekar and M. Pierri, Probing quantum gravity through ex- actly soluble minisuperspaces, J. Math. Phys., 37 (1996), 6250- 6270;
  11. [79]79. O. Aharony, S. Gubser, J. Maldacena, H. Ooguri, and Y. Oz, Large N theories, string theory and gravity, Phys. Rep., 323 (2000), 183- 386.

Cited by

Sorted by citations

Related

Authors
Ashtekar, A., Baez, J. C., & Krasnov, K.
Affiliations
  • Pennsylvania State University (US)
  • University of California, Riverside (US)
ORCID
Venue
Advances in Theoretical and Mathematical Physics
Publisher
International Press of Boston
Published
2000
Volume
4
Issue
1
Pages
1-94
ISSN
  • 1095-0753 (ISSN-L)
  • 1095-0761
DOI
10.4310/atmp.2000.v4.n1.a1
OpenAlex
W2150054850
Semantic Scholar
0aadaa53f13c4b760fd2b2cc502e438445037ac3
Cited by
580
References
70
Citations by year
2026: 9 · 2025: 29 · 2024: 11 · 2023: 8 · 2022: 7 · 2021: 16 · 2020: 8 · 2019: 11 · 2018: 20 · 2017: 23 · 2016: 26 · 2015: 22 · 2014: 32 · 2013: 23 · 2012: 23
FWCI
16.46
Type
journal article
Language
en
Open access
Locations
  • Advances in Theoretical and Mathematical Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (9722514, 9407194, 9514240)
  • University of Pennsylvania
  • Pennsylvania State 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 › Astronomy and Astrophysics › Relativity and Gravitational Theory
Keywords
isolated horizons, black hole entropy, quantum geometry, Chern-Simons theory, polymer quantization, non-rotating black holes, deficit angle, cosmological horizon, non-perturbative quantization

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