On the Degree of Sharpness in Solutions of Einstein's Field Equations

Details On the Degree of Sharpness in Solutions of Einstein's Field Equations On the Degree of Sharpness in Solutions of Einstein's Field Equations

Feb 1971

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1971rspsa.321..397w&link_type=abstract

Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 321, Issue 1546, pp. 397-408

Physics

3

Scientific paper

Einstein's theory of gravitation predicts that small changes in the gravitational field will propagate both sharply along the light cone and diffusively through its interior. In this paper the relative importance of sharp and diffusive propagation is linked to an invariant which arises in Sciama, Waylen & Gilman's integral formulation of Einstein's field equations. The invariant can be evaluated as an expansion in proper time, and the leading terms used to estimate the extent of diffusion. It is shown that, on a general empty space-time, the onset of diffusion is governed by a scalar related to the Bel-Robinson tensor. For some weak fields and all null fields this scalar may be equated to the covariant d'Alembertian of a gravitational density. On flat and plane wave space-times this quantity vanishes and the field equations satisfy a Huygens principle.

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