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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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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
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 ›
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