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Ll. Bel

Publications and source records attributed to Ll. Bel.

At least 37 records · Page 2Linked to original sources
arXiv2007

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.

gr-qc↗
arXiv2007

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.

gr-qc↗
arXiv2006

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.

gr-qc↗
arXiv2005

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.

physics.class-ph↗
arXiv2004

Isometry germs and related structures

We define an Isometry germ at any given event $x$ of space-time as a vector field $ξ$ 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.

gr-qc↗
arXiv2004

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.

gr-qc↗
arXiv2003

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 $ε$, the magnetic permeability $μ$, the unit of charge $e$, Plank's constant $h$, under the assumption of the constancy of the fine structure constant $α$, 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 $λ_c$ and their classical radius $r_0$.

gr-qc↗
arXiv2003

Eppur, si muove !

Simple ideas that shed new light on the physics of rotation as it concerns two famous experiments: The Wilson and Wilson, and the Michelson and Morley experiments.

gr-qc↗
arXiv2002

A New Look to Massive Neutron Cores

We reconsider the problem of modelling static spherically symmetric perfect fluid configurations with an equation of state from a point of view of that requires the use of the concept of principal transform of a 3-dimensional Riemannian metric. We discuss from this new point of view the meaning of those familiar quantities that we call density, pressure and geometry in a relativistic context. This is not simple semantics. To prove it we apply the new ideas to recalculate the maximum mass that a massive neutron core can have. This limit is found to be of the order of 3.8 $M_\odot$ substantially larger than the Oppenheimer and Volkoff limit.

gr-qc↗
arXiv2001

Extreme objects with arbitrary large mass, or density, and arbitrary size

We consider a generalization of the interior Schwarzschild solution that we match to the exterior one to build global C^1 models that can have arbitrary large mass, or density, with arbitrary size. This is possible because of a new insight into the problem of localizing the center of symmetry of the models and the use of principal transformations to understand the structure of space.

gr-qc↗
arXiv2001

Comparing metrics at large: harmonic vs quo-harmonic coordinates

To compare two space-times on large domains, and in particular the global structure of their manifolds, requires using identical frames of reference and associated coordinate conditions. In this paper we use and compare two classes of time-like congruences and corresponding adapted coordinates: the harmonic and quo-harmonic classes. Besides the intrinsic definition and some of their intrinsic properties and differences we consider with some detail their differences at the level of the linearized approximation of the field equations. The hard part of this paper is an explicit and general determination of the harmonic and quo-harmonic coordinates adapted to the stationary character of three well-know metrics, Schwarzschild's, Curzon's and Kerr's, to order five of their asymptotic expansions. It also contains some relevant remarks on such problems as defining the multipoles of vacuum solutions or matching interior and exterior solutions.

gr-qc↗
arXiv2000

Post-Newtonian Frames of Reference

A general theory of frames of reference proposed in a preceding publication is considered here in the framework of the post-Newtonian approximation, assuming that the frame of reference is centered on a time-like geodesic. The problem of taking into account the rotation of the frame of reference, which is usually ignored or incorrectly oversimplified, is here discussed in detail and solved.

gr-qc↗
arXiv1999

A Hierarchy of Dynamic States of Relaxation

We define a hierarchy of dynamic relaxed gas spheres as solutions of the Poisson equation coupled to a hierarchy of approximations of the Liouville equation leading, when this equation is satisfied, to the well-known isothermal gas spheres in the static case, but also to a new form of dynamic maximum relaxation. The two previous steps of the hierarchy correspond to an increasing degree of local relaxation at the center of the configuration.

gr-qc↗
arXiv1999

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.

gr-qc↗
arXiv1998

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.

gr-qc↗
arXiv1998

Regular order reductions of ordinary and delay-differential equations

We present a C program to compute by successive approximations the regular order reduction of a large class of ordinary differential equations, which includes evolution equations in electrodynamics and gravitation. The code may also find the regular order reduction of delay-differential equations.

physics.comp-ph↗
arXiv1998

The Froth of the Universe

We consider a model of the Universe based on the equation of state $p=(1/3)ρ(c/F)^2$, where $F$ is the scale factor. This model behaves as an inflationary Universe from the beginning and during its early stages, and behaves as dust matter during the stages of maximum expansion.

gr-qc↗