# Graviton-graviton scattering, Bel-Robinson and energy (pseudo)-tensors

@article{Deser1999GravitongravitonSB, title={Graviton-graviton scattering, Bel-Robinson and energy (pseudo)-tensors}, author={Stanley Deser and J. S. Franklin and Domenico Seminara}, journal={Classical and Quantum Gravity}, year={1999}, volume={16}, pages={2815-2821} }

Motivated by recent work involving the graviton-graviton tree scattering amplitude, and its twin descriptions as the square of the Bel-Robinson tensor, Bµ, and as the `current-current interaction' square of gravitational energy pseudo-tensors t, we find an exact tensor-square root equality , for a combination of Einstein and Landau-Lifschitz t, in Riemann normal coordinates. In the process, we relate, on-shell, the usual superpotential basis for classifying pseudo-tensors with one spanned by…

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## References

SHOWING 1-10 OF 10 REFERENCES

### Inconsistency of spin 4-spin 2 gauge field couplings

- Physics
- 1990

The authors invert the usual problem of coupling higher spin gauge fields to gravity by treating (linearised) gravity as the 'matter field' source of spin 4 gauge theory. This is motivated by the…

### COUNTERTERMS AND M-THEORY CORRECTIONS TO D = 11 SUPERGRAVITY

- Physics
- 1999

We construct a local on-shell invariant in D = 11 supergravity from the nonlocal four-point tree scattering amplitude. Its existence, together with earlier arguments, implies nonrenormalizability of…

### Normal forms for tensor polynomials. I. The Riemann tensor

- Mathematics
- 1992

Abstrael. Renormalization theoly in quantum gravity, among other applications, mntinues to stimulate many attempts 10 calculate asymptotic expansions of heat kernels and other Green functions of…

### Propagation laws for null and type III gravitational waves

- Physics, Mathematics
- 1960

Several algebraic characterizations of vacuum type III metric fields are discussed. A covariant integral conservation law is obtained by introducing a divergence free vector density that is uniquely…

### On the Bel - Robinson tensor

- Mathematics
- 1997

A completely symmetrical form of the Bel - Robinson (BR) tensor is shown to give rise, in n-dimensional Lorentzian space, to a gravitational density. For n = 4, a physical identification is proposed.

### LETTER TO THE EDITOR: Gauge invariance of Poincare generators in free higher spin gauge theories

- Physics
- 1990

The authors show that for any free symmetric tensor field model derived from a geometrical action by expansion about flat space, the unavoidable gauge dependence of its stress tensor is confined to a…

### Class

- Quant. Grav. 7, L119
- 1990

### hep-th/9812136

- Phys. Rev. Lett. 82 (1999) 2435; S. Deser and D. Seminara, “Constructing Invariants in and Nonrenormalizability of D=11 Supergravity,” BRX TH-456, to be submitted to Phys. Rev. D; S. Deser, gr-qc/9901007, to appear in Gravitation and Relativity in General,” World Publishing
- 1999

### Class

- Quant. Grav. 9
- 1992