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29 March 2024
 
  » arxiv » 1108.2277

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No Bel-Robinson Tensor for Quadratic Curvature Theories
S. Deser ; J. Franklin ;
Date 10 Aug 2011
AbstractWe attempt to generalize the familiar covariantly conserved Bel-Robinson tensor B ~ RR of GR and its recent topologically massive counterpart B ~ RDR, to quadratic curvature actions. Two very different models of current interest are examined: fourth order D=3 "new massive", and second order D>4 Gauss-Bonnet-Lovelock (GBL), gravity. On dimensional grounds, the candidates here become B ~ DRDR+RRR. For the D=3 model, there indeed exist conserved B ~ dR dR in the linearized limit. However, unlike for GR and TMG, and despite a plethora of available cubic terms, B cannot be extended to the full theory. The D>4 models are not even linearizable about flat space, since their field equations are quadratic in curvature; they also have no viable B, a fact that persists even if one includes cosmological or Einstein terms to allow linearization about the resulting dS vacua. These results are an unexpected, if hardly unique, example of non-linearization instability.
Source arXiv, 1108.2277
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