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MP: Theoretische und Mathematische Grundlagen der Physik

MP 12: Klassische Feldtheorie und Diff.geom. + topol. Aspekte

MP 12.3: Talk

Thursday, March 30, 2006, 15:00–15:30, P1-02-111

Tensor analysis with fractional derivatives and diffusion of gravitational waves — •Vladimir Kobelev — PB A203, Universität Siegen, Siegen D-57068

The variational principles with the partial fractional differentials are used for derivation of the field equations. The operator for static gravitation potential is the weighted sum of Laplace operator and elliptical Riesz potential operator, taken with the characteristic radius of field declination. In non-stationary case, the modified wave operator constitutes as sum of DAlembert wave operator and Riesz hyperbolical operator. The Green function for the wave equation with hereditary term is found. The general representation of the solution for fractional wave equation in form of retarded potentials is given. The solutions for the heredi-tary wave equation and classical wave equation are clearly distinctive in an important sense. The hereditary wave demonstrates the space diffusion of gravitational wave at the scales of metric constant. The diffusion leads to the blur of the peak and disruption of the sharp wave front. This contrasts with the solution of DAlembert classical wave equation, which obeys the Huygens principle and does not diffuse. The character of field declination - monotonic or oscillating - depends on the sign of the metric constant. The potential weakens more steeply, than the Newtonian potential. If the metric constant is negative, the hypothetical potential oscillates.