Abstract
It is shown that the new tensor identityrecently discovered by Bonanos, and some other tensoridentities recently investigated, are consequences of avery simple and mathematically trivial (but subtle) identity highlighted some years ago byLovelock. Lovelock's identity gives a tensor identity offirst order in Weyl-like tensors, and a tensor identityof second order in Ricci-like tensors, from which higher order identities, such as those recentlystudied, can easily be constructed.
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Edgar, S.B. Letter: Four-dimensional Tensor Identities of Low Order for the Weyl and Ricci Tensors. General Relativity and Gravitation 31, 405–411 (1999). https://doi.org/10.1023/A:1026601013194
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DOI: https://doi.org/10.1023/A:1026601013194