General relativity without the metric
Abstract
A new class of generally covariant gauge theories is introduced. The only field in addition to the gauge connection is a scalar-density Lagrange multiplier. For the group SO(3,C) [SO(3,R)] in four dimensions and particular coupling constants, the theory is equivalent to complex [Euclidean] general relativity, modulo an important degeneracy. The spacetime metric is constructed from the curvature in a solution. A canonical analysis leads directly to Ashtekar's Hamiltonian formalism. The general solution to the four diffeomorphism constraints in the nondegenerate case is given.
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Flat geometries are not contained in the sector of gravity described by the Capovilla-Dell-Jacobson formulation.
“In particular, flat geometries are not contained in this sector.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [109]
In the Capovilla-Dell-Jacobson formulation of general relativity, the integration over the e variables is partially performed at the continuum level.
“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 [109]
The Capovilla-Dell-Jacobson formulation corresponds to a sector of gravity in which the Weyl tensor satisfies certain algebraic requirements.
“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 [109]
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References 10 · Cited by 196
- Authors
- Capovilla, R., Jacobson, T., & Dell, J.
- Affiliations
- University of Maryland, College Park (US)
- ORCID
- Capovilla, Riccardo
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1989-11-20
- Volume
- 63
- Issue
- 21
- Pages
- 2325-2328
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W1966161082
- Cited by
- 196
- References
- 10
- Citations by year
- 2026: 1 · 2025: 4 · 2024: 2 · 2023: 3 · 2021: 6 · 2019: 3 · 2018: 4 · 2017: 1 · 2016: 3 · 2015: 12 · 2014: 3 · 2013: 5 · 2012: 4
- FWCI
- 23.24
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- Lagrange multipliers, canonical analysis, diffeomorphism constraint, degeneracy
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