Gravitomagnetic induction in the field of a gravitational wave

Abstract

The interaction of a plane gravitational wave with test masses can be described in the proper detector frame, using Fermi coordinates, in terms of a gravitoelectric and a gravitomagnetic field. We use this approach to calculate the displacements produced by gravitational waves up to second order in the distance parameter and, in doing so, we emphasize the relevance of the gravitomagnetic contribution related to gravitational induction. In addition, we show how this approach can be generalized to calculate displacements up to arbitrary order.

arXiv comment16 pages, LaTeX, 4 eps figures; revised to match the version accepted for publication by General Relativity and Gravitation

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• Analogy of space-time as an elastic medium -- Study of the perturbation tensor of the metric $h_{\mu \nu }$ through the prism of the analogy of the theory of elasticity -- Analysis and potential consequences
• A note on the description of plane gravitational waves in Fermi coordinates
• Quantum two-level systems and gravitational waves