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Cited by 704Black Holes and Theoretical PhysicsRelativity and Gravitational TheoryCosmology and Gravitation Theories

The gravitational Hamiltonian, action, entropy and surface terms

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Hawking, S W, Horowitz, Gary T·1996·Classical and Quantum Gravity
DOI 10.1088/0264-9381/13/6/017
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Abstract

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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Crossref · 10.1088/0264-9381/13/6/017

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  • This entropy bound is equivalent to the covariant entropy bound proposed in [31].

    “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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Research works printed but not linked: 2

  1. Gibbons G W 1986 in Fields and Geometry Proc. 22nd Karpacz Winter School of Theoretical Physics: Fields and Geometry (Karpacz, Poland, Febuary 17-March 1 1986) ed A Jadczyk (Singapore: World Scientific)
  2. Strominger A and Vafa C 1996 Preprint hep-th/9601029 · arXiv

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Authors
Hawking, S. W., & Horowitz, G. T.
Affiliations
  • University of Cambridge (GB)
  • University of California, Santa Barbara (US)
ORCID
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
DOI
10.1088/0264-9381/13/6/017
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
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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