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No Bel–Robinson tensor for quadratic curvature theories

Deser, S. and Franklin, J. (2011) No Bel–Robinson tensor for quadratic curvature theories. Classical and Quantum Gravity, 28 (23). Art. No.-235016. ISSN 0264-9381. doi:10.1088/0264-9381/28/23/235016.

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We attempt to generalize the familiar covariantly conserved Bel–Robinson tensor B_(μναβ) ~ RR of GR and its recent topologically massive third derivative order counterpart B ~ RDR to quadratic curvature actions. Two very different models of current interest are examined: fourth-order D = 3 'new massive gravity' and second-order D > 4 Lanczos–Lovelock. On dimensional grounds, the candidates here become B ~ DRDR + RRR. For the D = 3 model, there indeed exist conserved B ~ ∂R∂R in the linearized limit. However, 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 linearization instability.

Item Type:Article
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URLURL TypeDescription Paper
Deser, S.0000-0001-9285-9434
Additional Information:© 2011 IOP Publishing Ltd. Received 10 August 2011. Published 17 November 2011. SD acknowledges support from NSF PHY-1064302 and DOE DE-FG02-164 92ER40701 grants.
Group:Caltech Theory
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-16492ER40701
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Other Numbering System NameOther Numbering System ID
Issue or Number:23
Classification Code:PACS: 04.20.Cv, 04.50.−h, 04.50.Kd, 98.80.Cq. MSC: 83F05, 83C05
Record Number:CaltechAUTHORS:20120124-082154767
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Official Citation:No Bel–Robinson tensor for quadratic curvature theories S Deser and J Franklin doi:10.1088/0264-9381/28/23/235016
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:28928
Deposited By: Ruth Sustaita
Deposited On:24 Jan 2012 16:37
Last Modified:12 Jul 2022 19:40

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