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Spacetimes in which the Ricci equations characterize the Riemann tensor

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Abstract

It has recently been asked whether a fourth-order tensorK with all the algebraic symmetries of a Riemann tensor, and which satisfies the Ricci equations (with covariant derivative constructed from the metricg in the usual way), is always equal to the Riemann tensorR of the metricg; and a positive answer has been given for a generic tensorK in any nonflat 4-dimensional spacetime. In this paper it is shown that the result is also true in a generic 4-dimensional spacetime for any nontrivial tensorK. In addition, those special spacetimes where the result fails are given explicitly in terms of the Petrov types of their Weyl and Plebanski tensors.

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  1. Department of Mathematics, Linköping University, S-581 83, Linköping, Sweden

    S. Brian Edgar

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  1. S. Brian Edgar
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Edgar, S.B. Spacetimes in which the Ricci equations characterize the Riemann tensor. Int J Theor Phys 32, 121–135 (1993). https://doi.org/10.1007/BF00674400

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  • DOI: https://doi.org/10.1007/BF00674400

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