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No Bel-Robinson Tensor for Quadratic Curvature Theories | S. Deser
; J. Franklin
; | Date: |
10 Aug 2011 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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