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A pure spin-connection formulation of gravity
Open accessAbstract
A new action principle, in which the only gravitational variables are an SL(2,C) connection and a scalar density, is derived for general relativity (GR) coupled to matter and for supergravity. In this form, GR appears as a non-metric, generally covariant gauge theory, the metric being reconstructed from the other fields in a solution. A similar non-metric action with a real SO(3,1) connection is also derived, however it involves an independent fourth rank tensor field representing the curvature.
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“In particular, flat geometries are not contained in this sector.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [110]
In the citing paper
“In the Capovilla-Dell-Jacobson [110, 109] formulation of general relativity this ‘integration’ is partially performed at the continuum level.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [110]
In the citing paper
“One serious problem of this formulation is that it corresponds to a sector of gravity where the Weyl tensor satisfies certain algebraic requirements.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [110]
In the citing paper
“In the generic case, when the E ab (a < b) are linearly independent, it can be shown [20,22] that conditions (5) and (6) admit exactly three sorts of solutions in addition to those of the form”
From Spin foam models (1998) · cites this paper as [22]
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Metadata
- Authors
- Capovilla, R., Dell, J., & Jacobson, T.
- Affiliations
- University of Maryland, College Park (US)
- ORCID
- Capovilla, R
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1991-01-01
- Volume
- 8
- Issue
- 1
- Pages
- 59-73
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1972877551
- Cited by
- 162
- References
- 10
- Citations by year
- 2026: 2 · 2025: 1 · 2024: 2 · 2023: 3 · 2021: 4 · 2020: 2 · 2019: 3 · 2018: 1 · 2017: 3 · 2016: 5 · 2015: 10 · 2014: 3 · 2013: 5 · 2012: 3
- FWCI
- 21.45
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Geometry Research
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- general relativity, supergravity, Hamilton's principle, scalar density, metric reconstruction, matter coupling
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