dorsal/arxiv
View SchemaOn Higher Order Gravities, Their Analogy to GR, and Dimensional Dependent Version of Duff's Trace Anomaly Relation
| Authors | Mehrdad Farhoudi |
|---|---|
| Categories | |
| ArXiv ID | physics/0509210 |
| URL | https://arxiv.org/abs/physics/0509210 |
| DOI | 10.1007/s10714-006-0304-3 |
| Journal | Gen.Rel.Grav.38:1261-1284,2006 |
Abstract
An almost brief, though lengthy, review introduction about the long history of higher order gravities and their applications, as employed in the literature, is provided. We review the analogous procedure between higher order gravities and GR, as described in our previous works, in order to highlight its important achievements. Amongst which are presentation of an easy classification of higher order Lagrangians and its employment as a \emph{criteria} in order to distinguish correct metric theories of gravity. For example, it does not permit the inclusion of only one of the second order Lagrangians in \emph{isolation}. But, it does allow the inclusion of the cosmological term. We also discuss on the compatibility of our procedure and the Mach idea. We derive a dimensional dependent version of Duff's trace anomaly relation, which in \emph{four}-dimension is the same as the usual Duff relation. The Lanczos Lagrangian satisfies this new constraint in \emph{any} dimension. The square of the Weyl tensor identically satisfies it independent of dimension, however, this Lagrangian satisfies the previous relation only in three and four dimensions.
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"abstract": "An almost brief, though lengthy, review introduction about the long history\nof higher order gravities and their applications, as employed in the\nliterature, is provided. We review the analogous procedure between higher order\ngravities and GR, as described in our previous works, in order to highlight its\nimportant achievements. Amongst which are presentation of an easy\nclassification of higher order Lagrangians and its employment as a\n\\emph{criteria} in order to distinguish correct metric theories of gravity. For\nexample, it does not permit the inclusion of only one of the second order\nLagrangians in \\emph{isolation}. But, it does allow the inclusion of the\ncosmological term. We also discuss on the compatibility of our procedure and\nthe Mach idea. We derive a dimensional dependent version of Duff\u0027s trace\nanomaly relation, which in \\emph{four}-dimension is the same as the usual Duff\nrelation. The Lanczos Lagrangian satisfies this new constraint in \\emph{any}\ndimension. The square of the Weyl tensor identically satisfies it independent\nof dimension, however, this Lagrangian satisfies the previous relation only in\nthree and four dimensions.",
"arxiv_id": "physics/0509210",
"authors": [
"Mehrdad Farhoudi"
],
"categories": [
"physics.class-ph",
"gr-qc",
"hep-th"
],
"doi": "10.1007/s10714-006-0304-3",
"journal_ref": "Gen.Rel.Grav.38:1261-1284,2006",
"title": "On Higher Order Gravities, Their Analogy to GR, and Dimensional Dependent Version of Duff\u0027s Trace Anomaly Relation",
"url": "https://arxiv.org/abs/physics/0509210"
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