Born's group and Generalized isometries

We define the Born group as the group of transformations that leave invariant the line element of Minkowski's spacetime written in terms of Fermi coordinates of a Born congruence. This group depends on three arbitrary functions of a single argument. We construct implicitly the finite transformations of this group and explicitly the corresponding infinitesimal ones. Our analysis of this group brings out the new concept of Generalized group of isometries. The limitting cases of such groups being, at one end, the Groups of isometries of a spacetime metric and, at the other end, the Group of diffeomorphisms of any spacetime manifold. We mention two examples of potentially interesting generalizations of the Born congruences.Comment: In Proceedings of ERE93, Edited version, 9 page

A look inside the theory of the linear approximation

We introduce in the framework of the linear approximation of General relativity a natural distinction between General gauge transformations generated by any vector field and those Special ones for which this vector field is a gradient. This allows to introduce geometrical objects that are not invariant under General gauge transformations but they are under Special ones. We develop then a formalism that strengthens the analogy of the formalisms of the electromagnetic and the gravitational theories in a Special relativity framework. We are thus able to define the energy-momentum tensor of the gravitational field and to fully analyze the gravitational field of isolated point masses or continuous distributions of them obtained by linear superpositions.Comment: 14 pages, typos corrected, section replace

Reflections on three debated issues

A time-dependent model of space-time is used to suggest simple explanations for the increasing of the Astronomical unit, as well as the increasing of the distance from the Earth to the Moon. The Pioneer anomaly is also considered.Comment: 8 page

Gravitational waves signal analysis

I use a very simplified example to discuss the signature of a gravitational wave taking into account the relative state of motion of the detector with respect to the source that originated it. Something that to my knowledge has been ignored up to now and may ruin the best crafted template \cite{Templates}.Comment: 5 page

Isometry germs and related structures

We define an Isometry germ at any given event $x$ of space-time as a vector field $\xi$ defined in a neighborhood of $x$ such that the Lie derivative of both the metric and the Riemannian connection are zero at this event. Two isometry germs can be said to be equivalent if their values and the values of their first derivatives coincide at $x$. The corresponding quotient space can be endowed with a structure of a bracket algebra which is a deformation of de Sitter's Lie algebra. Each isometry germ defines also a local stationary frame of reference, the consideration of the family of adapted coordinate transformations between any two of them leading to a local novel structure that generalizes the Lorentz group.Comment: 17 page

Uber das Gravitationsfeld eines Massenpunktes nach der Einstenschen Theorie

Schwarzschild's solution of Einstein's field equations in vacuum can be written in many different forms. Unfortunately Schwarzschild's own original form is less nice looking and simple than that latter derived by Droste and Hilbert. We prove here that we can have both: a nice looking simple form and the meaning that Schwarzschild wanted to give to his solution, i.e., that of describing the gravitational field of a massive point particle.Comment: typos corrected, new reference, minor text modification

Phantom mass gravitational effects

I derive the basic relativistic corrections to the equations of motion of test particles and light rays in the field of a source with active mass $m$, including the phantom mass density that any such source generates when a modification of Newton's action at a distance includes a long range term. The technical framework of this paper is that of Einstein's theory of gravitation at the linear approximation with respect to the mass parameter $m$.Comment: 5 page

Space and Time models

We derive line-element's templates of space-time models with Space models complying with Helmholtz's Free mobility postulate, and discuss some of the Time models compatible with them.Comment: 11 pages, minor changes, an error in an intermediate step of the derivation of (40) has been correcte

Time dependence of c and its concomitants

As we showed in a preceding arXiv:gr-qc Einstein equations, conveniently written, provide the more orthodox and simple description of cosmological models with a time dependent speed of light $c$. We derive here the concomitant dependence of the electric permittivity $\epsilon$, the magnetic permeability $\mu$, the unit of charge $e$, Plank's constant $h$, under the assumption of the constancy of the fine structure constant $\alpha$, and the masses of elementary particles $m$. As a consequence of these concomitant dependences on time they remain constant their ratios $e/m$ as well as their Compton wave length $\lambda_c$ and their classical radius $r_0$.Comment: Latex, 11 page

Sensitivity of high precision Michelson-Morley experiments to tilting of their setups

We describe the effects to be expected of unwanted or voluntary deviations from the vertical of the axis of the active rotation of modern high precision experiments of the Michelson-Morley type. The theoretical description that we use is a particular implementation of the Principle of free mobility.Comment: Added reference