Publication at Faculty of Mathematics and Physics |
2014
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.