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

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

1999-05-06

arxiv.org/abs/gr-qc/9905021v1

Class.Quant.Grav.16:2815-2821,1999

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages

Scientific paper

10.1088/0264-9381/16/9/301

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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