Motivated by recent work involving the graviton-graviton tree scattering amplitude, and its twin descriptions as the square of the Bel-Robinson tensor, $B_{\m\n\a\b}$, and as the "current-current interaction" square of gravitational energy pseudo-tensors $t_{\a\b}$,we find an exact tensor-square root equality $B_{\mn\a\b} = \pa^2_\mn t_{\a\b}$, for a combination of Einstein and Landau-Lifschitz $t_\ab$, in Riemann normal coordinates. In the process, we relate, on-shell, the usual superpotential basis for classifying pseudo-tensors with one spanned by polynomials in the curvature.
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机译：受涉及引力子-引力树的散射幅度的最新研究的启发，其孪生描述为Bel-Robinson张量的平方，$ B _ {\ m \ n \ a \ b} $和“电流-电流相互作用”引力能量伪张量的平方$ t _ {\ a \ b} $，我们找到了精确的张量平方根等式$ B _ {\ mn \ a \ b} = \ pa ^ 2_ \ mn t _ {\ a \ b} $，表示爱因斯坦和Landau-Lifschitz $ t_ \ ab $的组合，以黎曼正态坐标表示。在这个过程中，我们在壳上关联了用伪曲张进行分类的通常的超势基础，伪张量的一个由多项式在曲率中跨越。
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