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

  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},
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… 

On the energy–momentum density of gravitational plane waves

By embedding Einstein's original formulation of general relativity into a broader context, we show that a dynamic covariant description of gravitational stress–energy emerges naturally from a

The Energy of Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics

According to the Einstein, Weinberg, and Møller energy-momentum complexes, we evaluate the energy distribution of the singularity-free solution of the Einstein field equations coupled to a suitable

Some remarks on the Bel‐Robinson tensor

In this paper we present our point of view on the correct physical interpretation of the Bel‐Robinson tensor within the framework of standard General Relativity (GR), i.e., within the framework of GR

Energy–momentum density in small regions: the classical pseudotensors

The values for the gravitational energy–momentum density, given by the famous classical pseudotensors: Einstein, Papapetrou, Landau–Lifshitz, Bergmann–Thompson, Goldberg, Møller and Weinberg, in the

Gravitational Energy-Momentum Density

In Teleparallel Gravity it is possible to obtain separate expressions for the energy-momentum density of gravity and of the interaction of gravity with inertial effects of the frame. The

Gravitational energy from a combination of a tetrad expression and Einstein's pseudotensor

The energy–momentum for a gravitating system can be considered using the tetrad teleparallel gauge current in orthonormal frames, instead of the more commonly used Einstein pseudotensor, which makes

Super-energy tensors

A simple and purely algebraic construction of super-energy (s-e) tensors for arbitrary fields is presented in any dimensions. These tensors have good mathematical and physical properties, and they

Perturbative Quantum Gravity and its Relation to Gauge Theory

  • Z. Bern
  • Physics
    Living reviews in relativity
  • 2002
A non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes is described and the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems.

Gravitational energy in a small region for the modified Einstein and Landau–Lifshitz pseudotensors

The purpose of the classical Einstein and Landau–Lifshitz and other pseudotensors is to determine the gravitational energy. Neither of them can guarantee a positive energy in holonomic frames. In the

Some remarks on the Bel-Robinson tensor and gravitational radiation

The asymptotic form of the Bel-Robinson tensor in the gravitational radiation-zone is obtained in terms of the mass quadrupole of the source. A comparison is made with the standard formula for the



Inconsistency of spin 4-spin 2 gauge field couplings

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


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

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

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

Normal forms for tensor polynomials. I. The Riemann tensor

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

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

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.


  • Quant. Grav. 7, L119
  • 1990


  • 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


  • Quant. Grav. 9
  • 1992