Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-07-04
Class. Quantum Grav. 29 (2012) 095006
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Title and content have been changed. To appear in CQG
Scientific paper
10.1088/0264-9381/29/9/095006
We take a Dirac field non-minimally coupled to the gravitational field within the framework of the Poincar\'e gauge theory of gravity with torsion and curvature. We study the subcase of "weak" gravity, that is, the gravitational Lagrangian depends only linearly on the curvature and quadratically on the torsion. We include all pieces in curvature and torsion that are of odd parity. The second field equation of gravity is derived by varying the Lorentz connection. We solve it with respect to the torsion and decompose the first field equation of gravity and the Dirac equation into Einsteinian pieces and post-Riemannian terms.
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