Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-03-02
Gen.Rel.Grav. 37 (2005) 343-363
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Scientific paper
10.1007/s10714-005-0023-1
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.
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