Victor H. Hamity

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

f(R) Cosmology in the First Order Formalism

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

Relativistic nonextensive kinetic theory

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

We construct an idealized spherically symmetric relativistic model of an exploding object within the framework of the theory of surface layers in GR. A Vaidya solution for a radially radiating star is matched through a spherical shell of dust to a Schwarzschild solution. The (incomplete) equations for the motion of the spherical shell of dust and the radiation density of the Vaidya solution, as given by the matching conditions, are reduced to a first-order system and a general analysis of the characteristics of the motion is given. This system of differential equations is completed, adding a relation between the unknowns which represents the simplest way to avoid an unphysical singularity in the motion. The results of a numerical integration of the equations are presented in two cases which we think may have some relationship to stellar explosions. A comparative set of results for other solutions is also given, and some possible generalizations of the model are pointed out.

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,

Uniform function constants of motion and their first-order perturbation

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