Local Cosmology

We define the concept of a Maximally symmetric osculating space-time at any event of any given Robertson-Walker model. We use this definition in two circumstances: i) to approximate any given cosmological model by a simpler one sharing the same observational parameters, i.e, the speed of light, the Hubble constant and the deceleration parameter at the time of tangency, and ii) to shed some light on the problem of considering an eventual influence of the overall behaviour of the Universe on localized systems at smaller scales, or viceversa.Comment: 13 pages, Latex. Corrected typo

Covariance and meaning

Several other factors, besides the intrinsic local geometry, contribute to give a meaning to a space-time model. The simplest example comes from comparing Minkowski's and Milne's model, that both have a null Riemann tensor. We add to these two models a third one which describes a time-dependent locally-Minkowskian spherically symmetric space-time on which every test-particle at rest with respect to the center of symmetry sustains a constant force. Although the model is globally grossly un-realistic we think that it can be helpful to describe a local perturbation of an homogeneous cosmological model. Or as a substitute to the very far away asymptotic Minkowskian behavior usually assumed to describe the gravitational field of compact spherical bodies.Comment: 10 pages, Corrected typos, Changed exampl

Do H_0 and q_0 really have the values we believe they have?

We present an example where a justified modification of the law of propagation of light in a Robertson-Walker model of the universe leads to an identification of H_0 and q_0 different from that corresponding to the usual law of propagation along null geodesics. We conclude from this example that observed values which we would associate with the values of H_0 and q_0 with the usual interpretation correspond in fact to the values of 2H_0 and $1/2 (q_0-1)$. It is therefore possible that observed values that we usually interpret as corresponding to a moderately aged universe with accelerating expansion may in fact correspond a much older universe with a decelerating expansion.Comment: Latex, 4 page

Testing a Crucial Assumption

Simplified description of an experiment of the Michelson-Morley type being completed at the University of Western Australia with a discussion of the possible meanings of its outcome.Comment: 14 page

Light Tides and the Kennedy-Thorndike experiments

We model the system Earth-Moon-Sun from the point of view of a frame of reference co-moving with the Earth and we derive a detailed prediction of the outcome of future Kennedy-Thorndike's type experiments to be seen as light tides.Comment: 14 page

Local cosmology of the solar system

A time-dependent model of space-time is used to describe the gravitational field of the sun. This model is a spherically symmetric approximate solution of Einstein's equations in vacuum. Near the sun it approximates one of the models derived from the Schwarzschild solution, while at large distances it becomes a milne's-like zero space-time curvature model. Two local cosmology free parameters provide simple descriptions for the secular increasing of the astronomical unit, as well as the "anomalous" radial acceleration of the Pioneer probe. We make also a comment about the possibility of deriving MOND's phenomenology from General relativity.Comment: 6 page

Basic cosmology

Basic cosmology describes the universe as a Robertson-Walker model filled with black-body radiation and no barionic matter, and as observational data it uses only the value of the speed of light, the Hubble and deceleration parameters and the black-body temperature at the present epoch. It predicts the value of the next new parameter in the Hubble law.Comment: 6 pages, 4 figure

Global SSS space-time models: MaM_a and QQ

To make sense of a global space-time model and to give a meaning to the coordinates that we use, a choice of a constant curvature space-metric of reference it is as much necessary as it is a choice of units of mass, length and time. The choice we make leads to contradict the belief that the exterior domain of a Static Spherically Symmetric (SSS) space-time model of finite radius $R$ depends only on the active mass $M_a$ of the source. In fact it depends on two parameters $M_a$ and a new one $Q$. We prove that both can be calculated as volume integrals extended over the whole space. We integrate Einstein's equations numerically in two simple cases: assuming either that the source of perfect fluid has constant proper density or that the pressure depends linearly on the proper density. We confirm a preceding paper showing that very compact objects can have active masses $M_a$ much greater than their proper masses $M_p$, and we conjecture that the mass point Fock's model can be understood as the limit of a sequence of compact models when both Q and its radius shrink to zero and the pressure equals the density

Frames of Reference and Some of its Applications

We define a Frame of reference as a two ingredients concept: A meta-rigid motion, which is a generalization of a Born motion, and a chorodesic synchronization, which is an adapted foliation. At the end of the line we uncover a low-level 3-dimensional geometry with constant curvature and a corresponding coordinated proper-time scale. We discuss all these aspects both from the geometrical point of view as from the point of view of some of the physical applications derived from them.Comment: Latex, 32 pages Journ-ref: To be published in "Gravitation and Relativity in General", Ed. A. Molina, J. Martin, E. Ruiz and F. Atrio. World Scientific (1999

Static elastic deformations in general relativity

We present a new approach to the theory of static deformations of elastic test bodies in general relativity based on a generalization of the concept of frame of reference which we identify with the concept of quo-harmonic congruence. We argue on the basis of this new approach that weak gravitational plane waves do not couple to elastic bodies and therefore the latter, whatever their shape, are not suitable antennas to detect them.Comment: 15 pages, Late