On relativistic deformable solids and the detection of gravitational waves |
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Authors: | Gérard A. Maugin |
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Affiliation: | 1. Département de Mécanique, E.R.A. du C.N.R.S., Université de Paris-VI, Tour 66-9, quai Saint-Bernard, 75005, Paris, France
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Abstract: | In this paper, the purpose of which is to complement a preceding work [1], it is shown, in agreement with the theory of relativistic deformable solids developed by A.C. Bringen and his coworkers, that the simplest conceivable dissipative constitutive equation — that of a socalled KelvinVoigt viscoelastic solid — yields a gravitational wave equation of propagation different from that of Weber: specifically, the following third order partial differential equation, $$frac{{partial ^2 theta }}{{partial t^2 }} - left( {A + A'frac{{partial ^2 theta }}{{partial t}}} right)frac{{partial ^2 theta }}{{partial x^2 }} = c^2 R_{1441'} $$ which can be solved by use of Fourier transform techniques, and where A and A′ are positive material coefficients. |
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