Torsion and Nonmetricity in Scalar-Tensor Theories of Gravity

We show that the gravitational field equations derived from an action composed of i) an arbitrary function of the scalar curvature and other scalar fields plus ii) connection-independent kinetic and source terms, are identical whether one chooses nonmetricity to vanish and have non-zero torsion or vice versa.Comment: 10 page

The Relativistic Factor in the Orbital Dynamics of Point Masses

There is a growing population of relativistically relevant minor bodies in the Solar System and a growing population of massive extrasolar planets with orbits very close to the central star where relativistic effects should have some signature. Our purpose is to review how general relativity affects the orbital dynamics of the planetary systems and to define a suitable relativistic correction for Solar System orbital studies when only point masses are considered. Using relativistic formulae for the N body problem suited for a planetary system given in the literature we present a series of numerical orbital integrations designed to test the relevance of the effects due to the general theory of relativity in the case of our Solar System. Comparison between different algorithms for accounting for the relativistic corrections are performed. Relativistic effects generated by the Sun or by the central star are the most relevant ones and produce evident modifications in the secular dynamics of the inner Solar System. The Kozai mechanism, for example, is modified due to the relativistic effects on the argument of the perihelion. Relativistic effects generated by planets instead are of very low relevance but detectable in numerical simulations

Relativistic Celestial Mechanics with PPN Parameters

Starting from the global parametrized post-Newtonian (PPN) reference system with two PPN parameters $\gamma$ and $\beta$ we consider a space-bounded subsystem of matter and construct a local reference system for that subsystem in which the influence of external masses reduces to tidal effects. Both the metric tensor of the local PPN reference system in the first post-Newtonian approximation as well as the coordinate transformations between the global PPN reference system and the local one are constructed in explicit form. The terms proportional to $\eta=4\beta-\gamma-3$ reflecting a violation of the equivalence principle are discussed in detail. We suggest an empirical definition of multipole moments which are intended to play the same role in PPN celestial mechanics as the Blanchet-Damour moments in General Relativity. Starting with the metric tensor in the local PPN reference system we derive translational equations of motion of a test particle in that system. The translational and rotational equations of motion for center of mass and spin of each of $N$ extended massive bodies possessing arbitrary multipole structure are derived. As an application of the general equations of motion a monopole-spin dipole model is considered and the known PPN equations of motion of mass monopoles with spins are rederived.Comment: 71 page

On Higher Order Gravities, Their Analogy to GR, and Dimensional Dependent Version of Duff's Trace Anomaly Relation

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 its important achievements. Amongst which are presentation of an easy classification of higher order Lagrangians and its employment as a \emph{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 \emph{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 \emph{four}-dimension is the same as the usual Duff relation. The Lanczos Lagrangian satisfies this new constraint in \emph{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.Comment: 30 pages, added reference

Inflation and Transition to a Slowly Accelerating Phase from S.S.B. of Scale Invariance

We consider the effects of adding a scale invariant $R^{2}$ term to the action of the scale invariant model (SIM) studied previously by one of us (E.I.G., Mod. Phys. Lett. A14, 1043 (1999)). The SIM belongs to the general class of theories, where an integration measure independent of the metric is introduced. To implement scale invariance (S.I.), a dilaton field is introduced. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (S.S.B) of S.I.. After S.S.B. of S.I. in the model with the $R^{2}$ term, it is found that a non trivial potential for the dilaton is generated. This potential contains two flat regions: one associated with the Planck scale and with an inflationary phase, while the other flat region is associated to a very small vacuum energy (V.E.) and is associated to the present slowly accelerated phase of the universe (S.A.PH). The smallness of the V.E. in the S.A.PH. is understood through the see saw mechanism introduced in S.I.M.Comment: 22 pages, latex, three figures now in separate file

Astrometry and geodesy with radio interferometry: experiments, models, results

Summarizes current status of radio interferometry at radio frequencies between Earth-based receivers, for astrometric and geodetic applications. Emphasizes theoretical models of VLBI observables that are required to extract results at the present accuracy levels of 1 cm and 1 nanoradian. Highlights the achievements of VLBI during the past two decades in reference frames, Earth orientation, atmospheric effects on microwave propagation, and relativity.Comment: 83 pages, 19 Postscript figures. To be published in Rev. Mod. Phys., Vol. 70, Oct. 199