English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

An almost brief, though lengthy, review introduction about the long historyof higher order gravities and their applications, as employed in theliterature, is provided. We review the analogous procedure between higher ordergravities and GR, as described in our previous works, in order to highlight itsimportant achievements. Amongst which are presentation of an easyclassification of higher order Lagrangians and its employment as a\emph{criteria} in order to distinguish correct metric theories of gravity. Forexample, it does not permit the inclusion of only one of the second orderLagrangians in \emph{isolation}. But, it does allow the inclusion of thecosmological term. We also discuss on the compatibility of our procedure andthe Mach idea. We derive a dimensional dependent version of Duff's traceanomaly relation, which in \emph{four}-dimension is the same as the usual Duffrelation. The Lanczos Lagrangian satisfies this new constraint in \emph{any}dimension. The square of the Weyl tensor identically satisfies it independentof dimension, however, this Lagrangian satisfies the previous relation only inthree and four dimensions.Comment: 30 pages, added reference

On higher order gravities, their analogy to GR, and dimensional dependent version of Duff’s trace anomaly relation