On a five-dimensional version of the Goldberg–Sachs theorem

0380306 - MÚ 2013 RIV GB eng J - Článek v odborném periodiku
Ortaggio, Marcello - Pravda, Vojtěch - Pravdová, Alena - Reall, H.
On a five-dimensional version of the Goldberg–Sachs theorem.
Classical and Quantum Gravity. Roč. 29, č. 20 (2012), s. 205002. ISSN 0264-9381. E-ISSN 1361-6382
Grant CEP: GA ČR GAP203/10/0749
Institucionální podpora: RVO:67985840
Klíčová slova: algebraic classification * Goldberg-Sachs theorem * higher dimensional Einstein equations
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 3.562, rok: 2012
http://iopscience.iop.org/0264-9381/29/20/205002

Previous work has found a higher dimensional generalization of the ‘geodesic part’ of the Goldberg–Sachs theorem. We investigate the generalization of the ‘shear-free part’ of the theorem. A spacetime is defined to be algebraically special if it admits a multiple Weyl aligned null direction (WAND). The algebraically special property restricts the form of the ‘optical matrix’ that defines the expansion, rotation and shear of themultipleWAND. After working out some general constraints that hold in arbitrary dimensions, we determine necessary algebraic conditions on the optical matrix of a multiple WAND in a five-dimensional Einstein spacetime. We prove that one can choose an orthonormal basis to bring the 3 × 3 optical matrix to one of three canonical forms, each involving two parameters, and we discuss the existence of an ‘optical structure’ within these classes. Examples of solutions corresponding to each form are given.
Trvalý link: http://hdl.handle.net/11104/0211046