Abstract
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.
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References
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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.
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Baranov, A.M. Algebraic classification of gravitational fields in five-dimensional space-time. Russ Phys J 38, 284–288 (1995). https://doi.org/10.1007/BF00559475
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DOI: https://doi.org/10.1007/BF00559475