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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 3 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. 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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