Quasi-Local Energy-Momentum and Angular Momentum in General Relativity
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The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed. First, the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities, are recalled. Then, the various specific constructions and their properties (both successes and deficiencies are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned.
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General Relativity has uncountably infinitely many symmetries of the action and thus, at least formally, infinitely many conserved currents.
“General Relativity has uncountably infinitely many symmetries of the action3 and thus, at least formally, infinitely many conserved currents”
From General Relativity, Mental Causation, and Energy Conservation (2022) · cites this paper as Szabados 2009
It remains uncertain whether a unique, consistent quasi-local definition of energy-momentum can be found that converges to a corresponding global one and remains consistent and unique as one moves progressively farther from a finite distribution of gravitational sources.
“However, it remains uncertain whether a unique, consistent quasi-local definition can be found that converges to a corresponding global one and remains consistent and unique as one moves progressively farther from a given finite distribution of gravitational sources.”
From A strictly local solution to the problem of energy in general relativity (2026) · cites this paper as Szabados, 2009
At least in cases with a non-zero cosmological constant, it is not true that there is no consensus in a large portion of the physics community about which is the preferred quasi-local expression.
“Furthermore, at least in cases with a non-zero cosmological constant, and pace Szabados (2009) which Lam cites, it is not really true that there is no consensus in-a large portion of-the physics community about which is the preferred expression 123”
From Noether's Theorems and Energy in General Relativity (2021) · cites this paper as Szabados (2009)
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References 638 · Cited by 351
Research works printed but not linked: 10
- [142]Chen, P.-N., Wang, M.-T. and Yau, S.-T., “Evaluating quasilocal energy and solving optimal embedding equation at null infinity”, arXiv, e-print, (2010). [arXiv:1002.0927]. (Cited on page 101.) · arXiv
- [278]Huisken G Ilmanen T The Riemannian Penrose inequality Int. Math. Res. Notices 1997 20 1045 1058 10.1155/S1073792897000664 · DOI
- [319]Kobayashi S Nomizu K Foundations of Differential Geometry, Vol. 2 1969 New York John Wiley
- [329]Kwong, K.-K., “On the positivity of a quasi-local mass in general dimensions”, arXiv, e-print, (2012). [arXiv:1207.7333]. (Cited on page 91.) · arXiv
- [335]Lau, S.R., “Lightcone embedding for quasilocal energy / Quasilocal boosts in general relativity”, Lectures given at the ‘International Workshop on Geometric Physics’, Physics and Mathematical Divisions, NCTS, Hsinchu, Taiwan, 24–26 July 2000, conference paper, (2000). (Cited on pages 90 and 92.)
- [344]Ludvigsen M Vickers JAG An inequality relating mass and electric charge in general relativity J. Phys. A: Math. Gen. 1983 16 1169 1174 10.1088/0305-4470/16/6/011 · DOI
- [374]Nahmad-Achar E Blair DG Buckingham MJ Is gravitational field energy density well defined for static, spherically symmetric configurations? The Fifth Marcel Grossmann Meeting on recent developments in theoretical and experimental general relativity, gravitation and relativistic field theories 1989 Singapore; River Edge, NJ World Scientific 1223 1225
- [395]Nielsen, A.B., “Black holes and black hole thermodynamics without event horizons”, arXiv, e-print, (2008). [arXiv:0809.3850 [hep-th]]. (Cited on page 120.) · arXiv
- [438]Rosenfeld, L., “Sur le tenseur d’impulsion-énergie”, Mem. R. Acad. Belg., Cl. Sci., 18 (6) (1940). (Cited on pages 12 and 21.)
- [504]’t Hooft G Ali A Ellis J Randjbar-Daemi S Dimensional reduction in quantum gravity Salamfestschrift 1994 Singapore; River Edge, NJ World Scientific
- Authors
- Szabados, L. B.
- Affiliations
- HUN-REN Wigner Research Centre for Physics (HU)
- Corresponding author
- Szabados, László B.
- ORCID
- Szabados, László B.
- Venue
- Living Reviews in Relativity
- Published
- 2009-06-19
- Volume
- 12
- Issue
- 1
- Pages
- 4-4
- ISSN
- 1433-8351 (ISSN-L)
- 2367-3613
- PMC
- PMC5256466
- OpenAlex
- W2123823073
- Cited by
- 351
- References
- 638
- Citations by year
- 2026: 9 · 2025: 42 · 2024: 22 · 2023: 16 · 2022: 23 · 2021: 23 · 2020: 26 · 2019: 33 · 2018: 26 · 2017: 21 · 2016: 23 · 2015: 20 · 2014: 19 · 2013: 8 · 2012: 15
- FWCI
- 0.88
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- cc-by
- Locations
- Living Reviews in Relativity (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- quasi-local mass, energy-momentum, angular momentum, general relativity, energy-momentum conservation, gravitational energy
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