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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Relative Motions of Free Test Particles in Robinson–Trautman Spacetimes of Any Dimension
verfasst von : Robert Švarc, Jiří Podolský
Erschienen in: Progress in Mathematical Relativity, Gravitation and Cosmology
Verlag: Springer Berlin Heidelberg
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Abstract
Using the invariant form of equation of geodesic deviation we analyze the relative deformations of a congruence of free test particles in general non-twisting, shearfree and expanding geometries. In four dimensions this class of exact solutions includes important classes of expanding gravitational waves. On the other hand, higher-dimensional Robinson–Trautman spacetimes can only be of algebraic type D. We emphasize the difference between the standard four-dimensional solutions and their arbitrary-dimensional extensions from the physical point of view of a geodesic observer.