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

Physical review D: Particles and fields (Impact Factor: 4.86). 07/2007; 76(8). DOI: 10.1103/PhysRevD.76.084025
Source: arXiv


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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    • "Here we explicitly show how the new geometrical structures in metric-affine gravity couple to matter, which in turn may underlie the design of experimental tests of gravity beyond the Einsteinian (purely Riemannian) geometrical picture. Our current work, generalizes and unifies several previous works [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] on the equations of motion in gauge gravity theories. "
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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.
    Preview · Article · Aug 2014 · Physical Review D
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    • "This clearly is a distinctive feature of theories which exhibit nonminimal coupling, which sets them apart from other gauge theoretical approaches to gravity. As we have shown in [6] [8] [9], and as it is also discussed at length in the recent review [19], in the minimally coupled case only microstructured matter couples to the post-Riemannian spacetime features – in particular, in the minimally coupled case one needs matter with intrinsic spin to detect the possible torsion of spacetime. As we have shown in the current work, this is no longer the case in the nonminimally coupled context. "
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    ABSTRACT: We derive multipolar equations of motion for gravitational theories with general nonminimal coupling in spacetimes admitting torsion. Our very general findings allow for the systematic testing of whole classes of theories by means of extended test bodies. One peculiar feature of certain subclasses of nonminimal theories turns out to be their sensitivity to post-Riemannian spacetime structures even in experiments without microstructured test matter.
    Preview · Article · Aug 2013 · Physical Review D
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    • "A short timeline of works can be found in [19]. Note that the model under consideration does not belong to the very general class of gravitational models analyzed in [19] due to its nonminimal coupling prescription. "
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    ABSTRACT: We present a covariant derivation of the equations of motion for test bodies for a wide class of gravitational theories with nonminimal coupling, encompassing a general interaction via the complete set of 9 parity-even curvature invariants. The equations of motion for spinning test bodies in such theories are explicitly derived by means of Synge's expansion technique. Our findings generalize previous results in the literature and allow for a direct comparison to the general relativistic equations of motion of pole-dipole test bodies.
    Preview · Article · Jan 2013 · Physical review D: Particles and fields
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