Computer Science
Scientific paper
Aug 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981gregr..13..731e&link_type=abstract
General Relativity and Gravitation, vol. 13, Aug. 1981, p. 731-745.
Computer Science
2
Gravitational Waves, Harmonic Generations, Nonlinear Equations, Perturbation Theory, Propagation Modes, Vacuum Effects, Coordinate Transformations, Free Fall, Particle Motion, Relativity, Space-Time Functions
Scientific paper
Linear and nonlinear perturbations of vacuum space-times are examined in the approximation of high frequencies. In order to do this, it is necessary to extend the concept of coordinate gauge transformations to the case of nonlinear terms. The generation of the second harmonic is studied by investigating perturbations of the tetrad components of the Weyl tensor. Propagation equations determining the amplitudes of these perturbations are derived. Finally, the relative motion in a system of test particles under the influence of both main wave and second harmonic as seen by a free falling observer is investigated. If inertial forces are absent, the second harmonic gives rise to oscillations in two transverse-traceless modes and in a transverse-scalar mode. The amplitude of the latter mode is proportional to the shear of the ray congruence along which the perturbations propagate.
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