First Order Formalism of f(R) Gravity

H. HAMITY AND D. BARRACO

GENERAL RELATIVITY AND GRAVITATION

Año: 1993 vol. 25 p. 461 - 471

0001-7701

{\bf--------------------------------------------------------------------------------------- }\\\noi The first order formalism is  applied to study the fieldequations of a general Lagrangian density for gravity of the form$L_G = \sqrt{- g}f(R)$.  These field equations correspond totheories which are a subclass of conformally metric theories inwhich the derivative of the metric is proportional to the metricby a Weyl vector field.  The resulting geometrical structure isunique, except when $f(R) = a R^2$, in the sense that theWeyl freld is identifiable in terms of the trace of theenergy-momentum tensor and its derivatives.  In the case $f(R)= a R^2$ the metric is only defined up to a conformal factor.We discuss the matter conservation equations which are implied bythe invariance of the theories under diffeomorphisms.  We applythe results to the case of dust and obtain that in general thedust particles will not follow geodesic lines.  We consider thelinearized field equations and apply them to obtain the weak fieldslow motion limit.  It is found that the gravitational potentialacquires a new term which depends linearly on the mass density.The importance of these new equations is briefly discussed. } \