Higher dimensional spacetimes with a geodesic, shearfree, twistfree and expanding null congruence

Abstract

We present the complete family of higher dimensional spacetimes that admit a geodesic, shearfree, twistfree and expanding null congruence, thus extending the well-known D=4 class of Robinson-Trautman solutions. Einstein's equations are solved for empty space with an arbitrary cosmological constant and for aligned pure radiation. Main differences with respect to the D=4 case (such as the absence of type III/N solutions, related to ``violations'' of the Goldberg-Sachs theorem in D>4) are pointed out, also in connection with other recent works. A formal analogy with electromagnetic fields is briefly discussed in an appendix, where we demonstrate that multiple principal null directions of null Maxwell fields are necessarily geodesic, and that in D>4 they are also shearing if expanding.

arXiv comment1+12 pages. Proceedings of the XVII SIGRAV Conference, Turin, September 4--7, 2006. v2: minor changes

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• Particle and light motion in a space-time of a five-dimensional rotating black hole
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• Static and radiating dyonic black holes coupled to conformally invariant electrodynamics in higher dimensions
• On the Weyl Tensor Classification in All Dimensions and its Relation with Integrability Properties
• Absence of gyratons in the Robinson-Trautman class
• Spinors and the Weyl Tensor Classification in Six Dimensions
• Higher dimensional Robinson-Trautman spacetimes sourced by p-forms: static and radiating black holes
• On the Pursuit of Generalizations for the Petrov Classification and the Goldberg-Sachs Theorem