Algebraic classification of gravitational fields in five-dimensional space-time

We consider the algebraic classification of five-dimensional empty space-time (Kalutsa type) with one time-like direction as a generalization of the Petrov algebraic classification of gravitational fields in four-dimensional space-time. 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 five-metric we introduce the pentad metric of a tangent five-space, which is mapped together with the curvature tensor into a ten-dimensional 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 sixth-order equation that can be simplified when certain requirements are satisfied. Our results demonstrate the nontrivial nature of algebraic classification in five dimensions.This work was performed within the framework of the State Science and Technology Astronomy program.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 73–78, March, 1995.