First order formalism of \(f(R)\) gravity
type: Item
instance of: scholarly article
title: First order formalism of \(f(R)\) gravity
zbMATH Open document ID: 0778.53055
DOI: 10.1007/BF00756965
author: Daniel E. Barraco
author: Víctor H. Hamity
published in: General Relativity and Gravitation
publication date: 1993-12-20T00:00:00Z
review text: The authors analyze a general class of geometrical theories of gravitation with a matter free Lagrangian of the form \({\mathcal L}=\sqrt{- g}\) \(f(R)\), where \(f\) is an arbitrary function of the curvature scalar \(R\). They assume arbitrary connection coefficients and vary the action considering the connections and the metric as independent fields. The resulting theory is a subclass of conformally metric theories of the Weyl type. It is found that except for the special case of general relativity, i.e. \(f(R)=R\) the strong equivalence principle is not true. The general theory has a weak field, small velocity limit that coincides with the Newtonian limit only if \(f''(0)=0\). If this last condition is not fulfilled, the deviation for the Newtonian value of the acceleration of a test body is proportional to the gradient of the mass density. The authors believe that such effects may be significant in the interior of a stellar system when thermodynamic configurations are rapidly changing.
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 83D05
zbMATH DE Number: 205364
zbMATH Keywords: conformally metric theories of the Weyl type
zbMATH Keywords: strong equivalence principle
zbMATH Keywords: Newtonian limit
zbMATH Keywords: thermodynamic configurations
reviewed by: Heinz Dehnen
MaRDI profile type: Publication
cites work: The nonlinear graviton in interaction with a photon
cites work: Unified geometric theory of electromagnetic and gravitational interactions
cites work: Variational formulation of general relativity from 1915 to 1925 ''Palatini's method'' discovered by Einstein in 1925
cites work: General Relativity
full work available at URL: https://doi.org/10.1007/bf00756965
OpenAlex ID: W1971859493
description: scientific article; zbMATH DE number 205364