The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
The gravitational Hamiltonian, action, entropy and surface terms
Open accessAbstract
We give a derivation of the gravitational Hamiltonian starting from the Einstein - Hilbert action, keeping track of all surface terms. This derivation can be applied to any spacetime that asymptotically approaches a static background solution. The surface term that arises in the Hamiltonian can be taken as the definition of the `total energy', even for spacetimes that are not asymptotically flat. (In the asymptotically flat case, it agrees with the usual ADM energy.) We also discuss the relation between the Euclidean action and the Hamiltonian when there are horizons of infinite area (e.g. acceleration horizons) as well as the usual finite area black hole horizons. Acceleration horizons seem to be more analogous to extreme than nonextreme black holes, since we find evidence that their horizon area is not related to the total entropy.
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“This result generalises a previous result of Hawking and Horowitz, who found the same formula for the Euclidean action of static Einstein-matter solutions with Λ = 0 and no conical singularities [67].”
From Vacuum metastability with black holes (2015) · cites this paper as [67]
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“This bound can easily be shown to be equivalent to the covariant entropy bound as proposed in [31].”
From Disturbing Implications of a Cosmological Constant (2002) · cites this paper as [31]
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Cites
Wald, R. M. (1984) · Cited by 6,274
Action integrals and partition functions in quantum gravity
Gibbons, G. W., & Hawking, S. W. (1977) · Physical Review D · doi:10.1103/physrevd.15.2752 · Cited by 3,449
Self-citationGeneral Relativity – An Einstein Centenary Survey
Irvine, J. M. (1980) · Physics Bulletin · doi:10.1088/0031-9112/31/4/029 · Cited by 2,872
Cosmic strings and domain walls
Vilenkin, A. (1985) · Physics Reports · doi:10.1016/0370-1573(85)90033-x · Cited by 2,096
Gravitation: an Introduction to current research
Witten, L. (1962) · CERN Document Server (European Organization for Nuclear Research) · Cited by 2,004
Quasilocal energy and conserved charges derived from the gravitational action
Brown, J. D., & York, J. W. (1993) · Physical Review D · doi:10.1103/physrevd.47.1407 · Cited by 1,793
(1979) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1,590
Self-citationRole of surface integrals in the Hamiltonian formulation of general relativity
Regge, T., & Teitelboim, C. (1974) · Annals of Physics · doi:10.1016/0003-4916(74)90404-7 · Cited by 1,424
Stability of gravity with a cosmological constant
Abbott, L. F., & Deser, S. (1982) · Nuclear Physics B · doi:10.1016/0550-3213(82)90049-9 · Cited by 1,075
Gravitation—An introduction to current research
Kilmister, C. W. (1963) · Planetary and Space Science · doi:10.1016/0032-0633(63)90130-2 · Cited by 729
Research works printed but not linked: 1
- Garfinkle D, 1991, Phys. Lett., 256B
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Thermodynamics of dynamical black holes beyond perturbation theory
Ashtekar, A., Paraizo, D. E., & Shu, J. (2026) · General Relativity and Gravitation · doi:10.1007/s10714-026-03585-4
Metadata
- Authors
- Hawking, S. W., & Horowitz, G. T.
- Affiliations
- University of Cambridge (GB)
- University of California, Santa Barbara (US)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1996-06-01
- Volume
- 13
- Issue
- 6
- Pages
- 1487-1498
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2042039466
- Cited by
- 704
- References
- 25
- Citations by year
- 2026: 9 · 2025: 21 · 2024: 18 · 2023: 18 · 2022: 22 · 2021: 15 · 2020: 15 · 2019: 35 · 2018: 31 · 2017: 8 · 2016: 13 · 2015: 23 · 2014: 14 · 2013: 20 · 2012: 37
- FWCI
- 16.86
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (9008502)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- Einstein-Hilbert action, surface terms, total energy, ADM energy, asymptotically flat spacetimes, Euclidean action, black hole entropy, acceleration horizon, extremal black holes, static background
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