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Graviton-Graviton Scattering, Bel-Robinson and Energy (Pseudo)-Tensors

S. Deser·J. S. Franklin·D. Seminara
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Abstract

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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S. Deser, J. S. Franklin, D. Seminara. 1999-05-06. Graviton-Graviton Scattering, Bel-Robinson and Energy (Pseudo)-Tensors. https://doi.org/10.1088/0264-9381%2F16%2F9%2F301

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