Type III and N Einstein spacetimes in higher dimensions : general properties

0348265 - MÚ 2011 RIV US eng J - Journal Article
Ortaggio, Marcello - Pravda, Vojtěch - Pravdová, Alena
Type III and N Einstein spacetimes in higher dimensions : general properties.
Physical Review D: Particles, Fields, Gravitation and Cosmology. Roč. 82, č. 6 (2010), 064043. ISSN 1550-7998
R&D Projects: GA ČR GAP203/10/0749
Institutional research plan: CEZ:AV0Z10190503
Keywords : higher-dimensional gravity * algebraic classification * Newman-Penrose formalism
Subject RIV: BA - General Mathematics
Impact factor: 4.964, year: 2010
http://journals.aps.org/prd/abstract/10.1103/PhysRevD.82.064043

The Sachs equations governing the evolution of the optical matrix of geodetic WANDs are explicitly solved in n dimensions in several cases which are of interest in potential applications. This is then used to study Einstein spacetimes of type III and N in the higher dimensional Newman-Penrose formalism, considering both Kundt and expanding solutions. In particular, the general dependence of the metric and of the Weyl tensor on an affine parameter r is obtained in a closed form. This allows us to characterize the peeling behaviour of the Weyl “physical” components for large values of r and thus to discuss, how the presence of twist affects polarization modes, and qualitative differences between four and higher dimensions. Further, the r dependence of certain nonzero scalar curvature invariants of expanding spacetimes is used to demonstrate that curvature singularities may generically be present.
Permanent Link: http://hdl.handle.net/11104/0188839