Newman-Penrose formalism in higher dimensions: vacuum spacetimes with a non-twisting geodetic multiple Weyl aligned null direction

dc.creatorPravdova, Alena
dc.creatorPravda, Vojtech
dc.date2008-06-15
dc.date2008-11-03
dc.date.accessioned2026-07-07T12:14:44Z
dc.date.available2026-07-07T12:14:44Z
dc.descriptionVacuum spacetimes admitting a non-twisting geodetic multiple Weyl aligned null direction (WAND) are analyzed in arbitrary dimension using recently developed higher-dimensional Newman-Penrose (NP) formalism. We determine dependence of the metric and of the Weyl tensor on the affine parameter r along null geodesics generated by the WAND for type III and N spacetimes and for a special class of type II and D spacetimes, containing e.g. Schwarzschild-Tangherlini black holes and black strings and branes. For types III and N, all metric components are at most quadratic polynomials in r while for types II and D the r-dependence of the metric as well as of the Weyl tensor is determined by an integer m corresponding to the rank of the expansion matrix S_{ij}. It is shown that for non-vanishing expansion, all these spacetimes contain a curvature singularity. As an illustrative example, a shearing expanding type N five-dimensional vacuum solution is also re-derived using higher-dimensional NP formalism. This solution can be, however, identified with a direct product of a known four-dimensional type N metric with an extra dimension.
dc.description25 pages, version to be published in Class. Quantum Grav. (expanded -background material included, 3 references added, small change in notation)
dc.identifierhttps://arxiv.org/abs/0806.2423
dc.identifierhttp://arxiv.org/abs/0806.2423
dc.identifierClass.Quant.Grav.25:235008,2008
dc.identifierdoi:10.1088/0264-9381/25/23/235008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/211296
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleNewman-Penrose formalism in higher dimensions: vacuum spacetimes with a non-twisting geodetic multiple Weyl aligned null direction
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