The Einstein Tensor and Its Generalizations

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  • David Lovelock
    Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada

Abstract

<jats:p>The Einstein tensor Gij is symmetric, divergence free, and a concomitant of the metric tensor gab together with its first two derivatives. In this paper all tensors of valency two with these properties are displayed explicitly. The number of independent tensors of this type depends crucially on the dimension of the space, and, in the four dimensional case, the only tensors with these properties are the metric and the Einstein tensors.</jats:p>

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