General relativity with spin and torsion and its deviations from Einstein's theory
Abstract
The field equations of general relativity with spin and torsion (${U}_{4}$ theory) are considered to describe correctly the gravitational properties of matter on a microphysical level. By an averaging procedure one arrives at a macroscopic field equation, which under normal matter densities coincides with Einstein's equation of conventional general relativity. For very high matter densities, even if the spin are randomly distributed, Einstein's equation breaks down and ${U}_{4}$ theory must be applied. It is shown how the singularity theorems of Penrose and Hawking must be modified to apply in ${U}_{4}$ theory. All known cosmological models in ${U}_{4}$ theory which prevent singularities are shown to violate an energy condition of a singularity theorem.
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Varying the action with respect to the metric and using the Cartan equations gives the Einstein field equations that relate the curvature of spacetime to the canonical energy-momentum tensor of matter.
“Varying the action with respect to the metric and using Equation (1) gives the Einstein field equations that relate the curvature of spacetime to the canonical energymomentum tensor of matter s ij ,”
From UNIVERSE IN A BLACK HOLE IN EINSTEIN–CARTAN GRAVITY (2016) · cites this paper as Hehl et al. 1974
If the spin orientation of particles in a spin fluid is random, then the last term on the right-hand side of Equation (6) vanishes after averaging, and the Einstein-Cartan equations for such a spin fluid are equivalent to the Einstein equations for a perfect fluid with effective energy density and pressure.
“If the spin orientation of particles in a spin fluid is random, then the last term on the right-hand side of Equation (6) vanishes after averaging.Thus, the Einstein-Cartan equations for such a spin fluid are equivalent to the Einstein equations for a perfect fluid with the effective energy density k s 4 2 and the effective pressure k p s 4 2 (Hehl et al. 1974;Kuchowicz 1978;Gasperini 1986;Bre”
From UNIVERSE IN A BLACK HOLE IN EINSTEIN–CARTAN GRAVITY (2016) · cites this paper as Hehl et al. 1974
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General relativity with spin and torsion: Foundations and prospects
Hehl, F. W., von der Heyde, P., Kerlick, G. D., & Nester, J. M. (1976) · Reviews of Modern Physics · doi:10.1103/revmodphys.48.393 · Cited by 2,709 · see citing works
Self-citationTesting general relativity in cosmology
Ishak, M. (2019) · Living Reviews in Relativity · doi:10.1007/s41114-018-0017-4 · Cited by 449 · see citing works
Cosmology with torsion: An alternative to cosmic inflation
Popławski, N. J. (2010) · Physics Letters B · doi:10.1016/j.physletb.2010.09.056 · Cited by 205 · see citing works
Nonsingular, big-bounce cosmology from spinor-torsion coupling
Popławski, N. (2012) · Physical Review D · doi:10.1103/physrevd.85.107502 · Cited by 180 · see citing works
UNIVERSE IN A BLACK HOLE IN EINSTEIN–CARTAN GRAVITY
Popławski, N. (2016) · The Astrophysical Journal · doi:10.3847/0004-637x/832/2/96 · Cited by 91 · see citing works
Kerlick, G. D. (1975) · Physical Review D · doi:10.1103/physrevd.12.3004 · Cited by 85 · see citing works
Self-citationA nonsingular, anisotropic universe in a black hole with torsion and particle production
Popławski, N. J. (2021) · General Relativity and Gravitation · doi:10.1007/s10714-021-02790-7 · Cited by 12 · see citing works
- Authors
- Hehl, F. W., von der Heyde, P., & Kerlick, G. D.
- Affiliations
- Princeton University (US)
- ORCID
- Hehl, Friedrich W.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1974-08-15
- Volume
- 10
- Issue
- 4
- Pages
- 1066-1069
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2171361875
- Cited by
- 213
- References
- 0
- Citations by year
- 2026: 7 · 2025: 14 · 2024: 13 · 2023: 13 · 2022: 3 · 2021: 10 · 2020: 11 · 2019: 13 · 2018: 12 · 2017: 8 · 2016: 4 · 2015: 6 · 2014: 8 · 2013: 7 · 2012: 6
- FWCI
- 7.43
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Keywords
- torsion, spin, averaging procedure, Penrose singularity theorem, energy conditions, cosmological models, singularity avoidance
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