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Motion of Test Particles in Spacetimes with Torsion and Nonmetricity

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arxiv 2310.15595 v1 pith:SKMVJLAS submitted 2023-10-24 gr-qc hep-th

Danianos Iosifidis , Friedrich W. Hehl This is my paper · ORCID
classification gr-qchep-th
keywords testnonmetricityparticletorsionmeansmotionspacetimesaccordingly
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abstract

We derive the equations of motion of a test particle with intrinsic hypermomentum in spacetimes with both torsion $S$ and nonmetricity $Q$ (along with curvature $R$). Accordingly, $S$ and $Q$ can be measured by tracing out the trajectory followed by a hypermomentum-charged test particle in such a non-Riemannian background. The test particle is approximated by means of a Dirac $\delta$-function. Thus we find a tangible way to observe and measure the effects of torsion and nonmetricity. Our results are consistent with earlier ones derived by Obukhov and Puetzfeld (2014) by means of a different method. We apply our insight and evaluate how far-reaching the so-called `geometrical trinity of gravity' really is.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Jacobson's thermodynamic approach to classical gravity applied to non-Riemannian geometries: remarks on the simplicity of Nature

    gr-qc 2026-01 unverdicted novelty 7.0 of 10

    Jacobson's thermodynamic approach applied to non-Riemannian geometries selects the Einstein-Hilbert action plus a quadratic torsion term as Nature's choice when non-metricity is absent and the metric energy-momentum t...

  2. `Translation invariant' black hole: autoparallels and complete integrability

    gr-qc 2025-06 conditional novelty 6.0 of 10

    Autoparallel motion in a class of torsionful Schwarzschild spacetimes is completely integrable via four conserved quantities, and positive-energy autoparallels are repelled by the black hole.

  3. Friedmann cosmology with hyperfluids

    gr-qc 2024-11 conditional novelty 6.0 of 10

    For a class of hyperfluid models in metric-affine gravity, the FLRW evolution of H(t) and rho(t) keeps the general relativity form, with hypermomentum effects encoded only in modified barotropic indices.

  4. Revisiting Coincident GR in Internal STEGR Formulation

    gr-qc 2025-06 conditional novelty 5.0 of 10

    The paper derives internal-STEGR field equations, recovers coincident GR as the coincident-gauge sector, and finds that massive test particles obey a norm-flow equation instead of geodesics.

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