How to lasso a plane gravitational wave

TL;DR

This paper models a relativistic elastic string in a gravitational wave background, demonstrating how gravitational curvature can excite natural frequencies and induce oscillations similar to spinning particles.

Contribution

It derives a relativistic string model in a Fermi frame and shows how gravitational waves can parametrically excite its natural frequencies and cause oscillations.

Findings

Gravitational curvature induces dominant acceleration terms dependent on position, velocity, and strain.

A ring-shaped string (lasso) has natural frequencies that can be parametrically excited by plane gravitational waves.

Oscillations proportional to spin magnitude and wave amplitude occur when the spin axis is in the wave front.

Abstract

Beginning with the stress-energy tensor of an elastic string this paper derives a relativistic string and its form in a parallel transported Fermi frame including its reduction in the Newtonian limit to a Cosserat string. In a Fermi frame gravitational curvature is seen to induce three dominant relative acceleration terms dependent on: position, velocity and position, strain and position, respectively. An example of a string arranged in an axially flowing ring (a lasso) is shown to have a set of natural frequencies that can be parametrically excited by a monochromatic plane gravitational wave. The lasso also exhibits, in common with spinning particles, oscillation about geodesic motion in proportion to spin magnitude and wave amplitude when the spin axis lies in the gravitational wave front. Coordinate free notation is used throughout including the development of the properties of the Fermi frame.