Algebraic classification of gravitational fields in fivedimensional spacetime
Abstract
We consider the algebraic classification of fivedimensional “empty” spacetime (Kalutsa type) with one timelike direction as a generalization of the Petrov algebraic classification of gravitational fields in fourdimensional spacetime. We study two special cases: a) zero electromagnetic field and zero scalar field; b) nonzero electromagnetic field and zero scalar field. For the (1+4) separated Kalutsa fivemetric we introduce the pentad metric of a tangent fivespace, which is mapped together with the curvature tensor into a tendimensional real flat vector space. The classification is constructed in local geodesic coordinates for the above two cases. In both cases the characteristic equation can be reduced to a sixthorder equation that can be simplified when certain requirements are satisfied. Our results demonstrate the nontrivial nature of algebraic classification in five dimensions.
 Publication:

Russian Physics Journal
 Pub Date:
 March 1995
 DOI:
 10.1007/BF00559475
 Bibcode:
 1995RuPhJ..38..284B