Einstein manifolds with torsion and nonmetricity
| Autor: | Dietmar Klemm, Lucrezia Ravera |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
Mathematics - Differential Geometry Scalar (mathematics) FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) 01 natural sciences General Relativity and Quantum Cosmology Gravitation symbols.namesake 0103 physical sciences FOS: Mathematics Einstein 010306 general physics Mathematical Physics Ricci curvature Mathematical physics Physics 010308 nuclear & particles physics torsion Equations of motion Mathematical Physics (math-ph) Einstein manifolds torsion nonmetricity Nonmetricity tensor Manifold Conformal gravity nonmetricity Einstein manifolds High Energy Physics - Theory (hep-th) Differential Geometry (math.DG) symbols Mathematics::Differential Geometry |
| Zdroj: | Physical Review D. 101 |
| ISSN: | 2470-0029 2470-0010 |
| DOI: | 10.1103/physrevd.101.044011 |
| Popis: | Manifolds endowed with torsion and nonmetricity are interesting both from the physical and the mathematical points of view. In this paper, we generalize some results presented in the literature. We study Einstein manifolds (i.e., manifolds whose symmetrized Ricci tensor is proportional to the metric) in d dimensions with nonvanishing torsion that has both a trace and a traceless part, and analyze invariance under extended conformal transformations of the corresponding field equations. Then, we compare our results to the case of Einstein manifolds with zero torsion and nonvanishing nonmetricity, where the latter is given in terms of the Weyl vector (Einstein-Weyl spaces). We find that the trace part of the torsion can alternatively be interpreted as the trace part of the nonmetricity. The analysis is subsequently extended to Einstein spaces with both torsion and nonmetricity, where we also discuss the general setting in which the nonmetricity tensor has both a trace and a traceless part. Moreover, we consider and investigate actions involving scalar curvatures obtained from torsionful or nonmetric connections, analyzing their relations with other gravitational theories that appeared previously in the literature. In particular, we show that the Einstein-Cartan action and the scale invariant gravity (also known as conformal gravity) action describe the same dynamics. Then, we consider the Einstein-Hilbert action coupled to a three-form field strength and show that its equations of motion imply that the manifold is Einstein with totally antisymmetric torsion. Comment: 27 pages, Accepted for publication in Phys. Rev. D |
| Databáze: | OpenAIRE |
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