Physics
Scientific paper
Mar 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987cqgra...4..253e&link_type=abstract
Classical and Quantum Gravity (ISSN 0264-9381), vol. 4, March 1, 1987, p. 253-264. Research supported by the Alexander von Humbo
Physics
16
Cosmic Dust, Gravitational Fields, Gravitational Waves, Matter (Physics), Wave Propagation, Einstein Equations, Perturbation Theory, Space-Time Functions, Wave Dispersion, Wentzel-Kramer-Brillouin Method
Scientific paper
The propagation of small-amplitude gravitational waves through pressureless matter ('dust') is investigated. After establishing the local linearization stability of Einstein's equation for dust about any of its solutions, the geometrical optics methods is used to study the locally plane, linearized perturbations of an arbitrary background dust spacetime asymptotically for small wavelengths. The dispersion relation exhibits two modes. One is simply degenerate and represents gravitational waves, whereas the other is doubly degenerate and describes density and vorticity perturbations. The waves are shown to propagate along the null geodesics of the background; in leading geometrical optics order, their amplitudes behave as in vacuo. The rays associated with the matter mode are the worldlines of the background dust. In leading order the perturbations of density and four-velocity vanish for both modes.
Breuer R. A.
Ehlers Juergen
Prasanna A. R.
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