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Riemann normal coordinates, Fermi reference system and the geodesic deviation equation

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arxiv gr-qc/0010096 v1 pith:B4H5M6H2 submitted 2000-10-26 gr-qc

Alexander I. Nesterov This is my paper · ORCID
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keywords coordinatesferminormaldeviationgeodesicmetricriemannsystem
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We obtain the integral formulae for computing the tetrads and metric components in Riemann normal coordinates and Fermi coordinate system of an observer in arbitrary motion. Our approach admits essential enlarging the range of validity of these coordinates. The results obtained are applied to the geodesic deviation in the field of a weak plane gravitational wave and the computation of plane-wave metric in Fermi normal coordinates.

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Cited by 2 Pith papers

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  1. Cosmological perturbations meet Wheeler DeWitt

    hep-th 2024-12 conditional novelty 6.0 of 10

    The semiclassical Wheeler-DeWitt wavefunction matches the perturbation-theory wavefunction of cosmology up to a specific phase and normalization, verified in exponential-potential and slow-roll mini-superspace models.

  2. Equivalence Principle violation in metric-affine gravity and finite-temperature effects

    gr-qc 2026-06 unverdicted novelty 4.0 of 10

    Metric-affine gravity formulates equivalence principle violations via non-metricity that parallel finite-temperature mass-ratio shifts, and a generalized Fermi-Walker derivative shows no orthonormal tetrad propagates ...

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