Gravitomagnetic induction in the field of a gravitational wave

TL;DR

This paper explores how gravitational waves induce displacements in test masses by analyzing gravitoelectric and gravitomagnetic fields, highlighting the significance of gravitomagnetic effects and providing a method for higher-order calculations.

Contribution

It introduces a framework for calculating gravitational wave-induced displacements up to any order, emphasizing the role of gravitomagnetic induction in the proper detector frame.

Findings

Gravitomagnetic effects are significant in gravitational wave detection.

Displacements can be calculated to arbitrary order using the proposed approach.

Second-order calculations reveal important gravitomagnetic contributions.

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.