https://doi.org/10.1140/epjp/s13360-023-04424-0
Regular Article
A note on the description of plane gravitational waves in Fermi coordinates
1
Dipartimento di Matematica “G.Peano”, Università degli studi di Torino, Via Carlo Alberto 10, 10123, Torino, Italy
2
INFN - LNL, Viale dell’Università 2, 35020, Legnaro, PD, Italy
a
matteoluca.ruggiero@unito.it
Received:
7
July
2023
Accepted:
30
August
2023
Published online:
8
September
2023
We use the formalism of Fermi coordinates to describe the interaction of a plane gravitational wave in the proper detector frame. In doing so, we emphasize that in this frame the action of the gravitational wave can be explained in terms of a gravitoelectromagnetic analogy. In particular, up to linear displacements from the reference world-line, the effects of the wave on test masses can be described in terms of a Lorentz-like force equation. In this framework, we focus on the effects on time measurements provoked by the passage of the wave, and evaluate their order of magnitude. Eventually, we calculate the expression of the local spacetime metric in cylindrical coordinates adapted to the symmetries of the gravitational field and show its relevance in connection with the helicity–rotation coupling.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
