On the separation of Einsteinian substructures
Abstract
Within the spinorial version of the Cartan structure formulas with the built-in (complex) Einstein vacuum equations some closed semi-Einsteinian substructures are isolated and discussed. Then the idea of semigraviton is introduced, and its relationship to Penrose’s nonlinear graviton is described.
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The Plebanski Lagrangian for general relativity has the form of BF theory with gauge group SL(2,C), with an added term which is a constraint.
“In fact, the Plebanski Lagrangian [8,9] for general relativity has the form of BF theory [10] with gauge group SL(2 , C ), with an added term which is a constraint.”
From Relativistic spin networks and quantum gravity (1998) · cites this paper as [8]
Plebanski demonstrated that the action for self-dual Riemannian gravity can be expressed as an SU(2) BF theory with constraints.
“According to Plebanski [307], the action of self-dual Riemannian gravity can be written as a constrained SU(2) BF theory”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [307]
Plebanski's Riemannian action for general relativity can be thought of as Spin(4) BF theory plus constraints on the B-field.
“Our starting point is Plebanski’s Riemannian action for general relativity, which can be thought of as Spin(4) BF theory plus constraints on the B-field.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [307]
The new spin-foam models are based on Plebanski's realization that classical general relativity can be obtained by suitably constraining the variations of the B field in BF theory.
“The new spin-foam models are based on Plebanski’s realization that one can obtain classical general relativity by suitably constraining the variations of the B field in the simple kind of topological theory called BF theory [307].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [307]
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- Authors
- Plebański, J. F.
- Affiliations
- Centro de Investigación y de Estudios Avanzados del I.P.N., México D.F., 14−740, México
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1977-12-01
- Volume
- 18
- Issue
- 12
- Pages
- 2511-2520
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2024934212
- Cited by
- 499
- References
- 0
- Citations by year
- 2026: 7 · 2025: 18 · 2024: 18 · 2023: 19 · 2022: 10 · 2021: 18 · 2020: 15 · 2019: 11 · 2018: 17 · 2017: 15 · 2016: 21 · 2015: 18 · 2014: 13 · 2013: 30 · 2012: 25
- FWCI
- 1.29
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Mathematical Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- vacuum Einstein equations, closed submanifolds
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