Bel–Robinson tensor
In general relativity and differential geometry, the Bel–Robinson tensor is a tensor defined in the abstract index notation by: T a b c d = C a e c f C b e d f + 1 4 ϵ a e h i ϵ b e j k C h i c f C j k d f {\displaystyle T_{abcd}=C_{aecf}C_{b}{}^{e}{}_{d}{}^{f}+{\frac {1}{4}}\epsilon _{ae}{}^{hi}\epsilon _{b}{}^{ej}{}_{k}C_{hicf}C_{j}{}^{k}{}_{d}{}^{f}} Alternatively, T a b c d = C a e c f C b e d f − 3 2 g a [ b C j k ] c f C j k d f {\displaystyle T_{abcd}=C_{aecf}C_{b}{}^{e}{}_{d}{}^{f}-{\frac {3}{2}}g_{a[b}C_{jk]cf}C^{jk}{}_{d}{}^{f}} where C a b c d {\displaystyle C_{abcd}} is the Weyl tensor. It was introduced by Lluís Bel in 1959.