Daniel E. Barraco

Newtonian limit of the singular f(R) gravity in the Palatini formalism

Recently D. Vollick [Phys. Rev. D68, 063510 (2003)] has shown that the inclusion of the 1/R curvature terms in the gravitational action and the use of the Palatini formalism offer an alternative explanation for cosmological acceleration. In this work we show not only that this model of Vollick does not have a good Newtonian limit, but also that any f(R) theory with a pole of order n in R=0 and its second derivative respect to R evaluated at Ro is not zero, where Ro is the scalar curvature of background, does not have a good Newtonian limit.

First order formalism off(R) gravity

AbstractThe first order formalism is applied to study the field equations of a general Lagrangian density for gravity of the form

Hydrostatic equilibrium equation and Newtonian limit of the singular f(R) gravity

\mathcal{L}_G = \sqrt { - g} f(R)

The Newtonian limit in a family of metric affine theories of gravitation

. These field equations correspond to theories which are a subclass of conformally metric theories in which the derivative of the metric is proportional to the metric by a Weyl vector field. The resulting geometrical structure is unique, except whenf(R)=aR2, in the sense that the Weyl field is identifiable in terms of the trace of the energy-momentum tensor and its derivatives. In the casef(R)=aR2 the metric is only defined up to a conformai factor. We discuss the matter conservation equations which are implied by the invariance of the theories under diffeomorphisms. We apply the results to the case of dust and obtain that in general the dust particles will not follow geodesic Unes. We consider the linearized field equations and apply them to obtain the weak field slow motion limit. It is found that the gravitational potential acquires a new term which depends linearly on the mass density. The importance of these new equations is briefly discussed.

The energy concept and the binding energy in a class of scalar--tensor theories of gravity

AbstractIn the present work we consider those theories that are obtained from a Lagrangian density ℒT(R) = f(R)√{-g} + ℒM, that depends on the curvature scalar and a matter Lagrangian that does not depend on the connection, and apply Palatinis method to obtain the field equations. We start with a brief discussion of the field equations of the theory and apply them to a cosmological model described by the FRW metric. Then, we introduce an auxiliary metric to put the resultant equations into the form of GR with cosmological constant and coupling constant that are curvature depending. We show that we reproduce known results for the quadratic case. We find relations among the present values of the cosmological parameters q0, H0,

Relativistic dynamics of cylindrical shells of counter-rotating particles

\mathop {(G/G)}\limits^ \circ _0