Propagation equations for deformable test bodies with microstructure in extended theories of gravity

Physical review D: Particles and fields 07/2007; 76(8). DOI: 10.1103/PhysRevD.76.084025
Source: arXiv

ABSTRACT We derive the equations of motion in metric-affine gravity by making use of the conservation laws obtained from Noether's theorem. The results are given in the form of propagation equations for the multipole decomposition of the matter sources in metric-affine gravity, i.e., the canonical energy-momentum current and the hypermomentum current. In particular, the propagation equations allow for a derivation of the equations of motion of test particles in this generalized gravity theory, and allow for direct identification of the couplings between the matter currents and the gauge gravitational field strengths of the theory, namely, the curvature, the torsion, and the nonmetricity. We demonstrate that the possible non-Riemannian spacetime geometry can only be detected with the help of the test bodies that are formed of matter with microstructure. Ordinary gravitating matter, i.e., matter without microscopic internal degrees of freedom, can probe only the Riemannian spacetime geometry. Thereby, we generalize previous results of general relativity and Poincare gauge theory. Comment: 27 pages, 1 figure, matches published version including the erratum in Phys. Rev. D 79 (2009) 069902(E)

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    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.
    Physical Review D 08/2014; 90(8). DOI:10.1103/PhysRevD.90.084034 · 4.86 Impact Factor
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    Physical Review D 08/2013; 88(6). DOI:10.1103/PhysRevD.88.064025 · 4.86 Impact Factor
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