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Journal of Mathematical Physics / Volume 12 / Issue 3

J. Math. Phys. 12, 498 (1971); http://dx.doi.org/10.1063/1.1665613 (4 pages)

The Einstein Tensor and Its Generalizations

David Lovelock

Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada

(Received 27 August 1970)

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.

© 1971 The American Institute of Physics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.1665613

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef The American Institute of Physics

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