caa a22 4500 46788756X CHVBK 20180406152739.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10714-006-0304-3 doi (NATIONALLICENCE)springer-10.1007/s10714-006-0304-3 Farhoudi Mehrdad Department of Physics, Shahid Beheshti University, 1983963113, Tehran, Evin, Iran aut On higher order gravities, their analogy to GR, and dimensional dependent version of Duff's trace anomaly relation [Elektronische Daten] [Mehrdad Farhoudi] 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/manipulate its important achievements. Amongst which are presentation of an easy classification of higher order Lagrangians and its employment as a 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 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 four-dimension is the same as the usual Duff relation. The Lanczos Lagrangian satisfies this new constraint in 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. Springer Science and Business Media, Inc., 2006 Higher order gravity nationallicence Non-linear Lagrangian nationallicence Weyl anomaly nationallicence General Relativity and Gravitation Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 38/8(2006-08-01), 1261-1284 0001-7701 38:8<1261 2006 38 10714 https://doi.org/10.1007/s10714-006-0304-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-006-0304-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Farhoudi Mehrdad Department of Physics, Shahid Beheshti University, 1983963113, Tehran, Evin, Iran aut NATIONALLICENCE 773 0- General Relativity and Gravitation Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 38/8(2006-08-01), 1261-1284 0001-7701 38:8<1261 2006 38 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer