Equations of motion in metric-affine gravity: A covariant unified framework
arXiv:1408.5669 · doi:10.1103/PhysRevD.90.084034
Abstract
We derive the equations of motion of extended deformable bodies in metric-affine gravity. The conservation laws which follow from the invariance of the action under the general coordinate transformations are used as a starting point for the discussion of the dynamics of extended deformable test bodies. By means of a covariant approach, based on Synge's world function, we obtain the master equation of motion for an arbitrary system of coupled conserved currents. This unified framework is then applied to metric-affine gravity. We confirm and extend earlier findings; in particular, we once again demonstrate that it is only possible to detect the post-Riemannian spacetime geometry by ordinary (non-microstructured) test bodies if gravity is nonminimally coupled to matter.
arXiv comment13 pages, RevTex format. Dedicated to Friedrich W. Hehl on the occasion of his birthday
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