Centre de masses relativista per a sistemes de partícules amb interacció directa

The center of mass problem for interacting relativistic particle systems is studied. It is shown the impossibility of finding —in the relativistic case— a set of three coordinate functions satisfying similar conditions to those verified by the Newtonian center of mass. Finally a particular system is studied and its center of mass is given according to restrictions previously set

Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models

The consistency of the constraint with the evolution equations for spatially inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands that the former are preserved along the timelike congruence represented by the velocity of the dust fluid, leading to \emph{new} non-trivial constraints. This fact has been used to conjecture that the resulting models correspond to the spatially homogeneous (SH) models of Bianchi type I, at least for the case where the cosmological constant vanish. By exploiting the full set of the constraint equations as expressed in the 1+3 covariant formalism and using elements from the theory of the spacelike congruences, we provide a direct and simple proof of this conjecture for vacuum and dust fluid models, which shows that the Szekeres family of solutions represents the most general class of SIIS models. The suggested procedure also shows that, the uniqueness of the SIIS of the Petrov type D is not, in general, affected by the presence of a non-zero pressure fluid. Therefore, in order to allow a broader class of Petrov type I solutions apart from the SH models of Bianchi type I, one should consider more general ``silent'' configurations by relaxing the vanishing of the vorticity and the magnetic part of the Weyl tensor but maintaining their ``silence'' properties i.e. the vanishing of the curls of $E_{ab},H_{ab}$ and the pressure $p$.Comment: Latex, 19 pages, no figures;(v2) some clarification remarks and an appendix are added; (v3) minor changes to match published versio

A classification of spherically symmetric spacetimes

A complete classification of locally spherically symmetric four-dimensional Lorentzian spacetimes is given in terms of their local conformal symmetries. The general solution is given in terms of canonical metric types and the associated conformal Lie algebras. The analysis is based upon the local conformal decomposition into 2+2 reducible spacetimes and the Petrov type. A variety of physically meaningful example spacetimes are discussed

Flat deformation theorem and symmetries in spacetime

The \emph{flat deformation theorem} states that given a semi-Riemannian analytic metric $g$ on a manifold, locally there always exists a two-form $F$, a scalar function $c$, and an arbitrarily prescribed scalar constraint depending on the point $x$ of the manifold and on $F$ and $c$, say $\Psi (c, F, x)=0$, such that the \emph{deformed metric} $\eta = cg -\epsilon F^2$ is semi-Riemannian and flat. In this paper we first show that the above result implies that every (Lorentzian analytic) metric $g$ may be written in the \emph{extended Kerr-Schild form}, namely $\eta_{ab} := a g_{ab} - 2 b k_{(a} l_{b)}$ where $\eta$ is flat and $k_a, l_a$ are two null covectors such that $k_a l^a= -1$; next we show how the symmetries of $g$ are connected to those of $\eta$, more precisely; we show that if the original metric $g$ admits a Conformal Killing vector (including Killing vectors and homotheties), then the deformation may be carried out in a way such that the flat deformed metric $\eta$ `inherits' that symmetry.Comment: 30 pages, 0 figure

Flat deformation of a spacetime admitting two Killing fields

It is shown that given an analytic Lorentzian metric on a 4-manifold, $g$, which admits two Killing vector fields, then it exists a local deformation law $\eta = a g + b H$, where $H$ is a 2-dimensional projector, such that $\eta$ is flat and admits the same Killing vectors. We also characterize the particular case when the projector $H$ coincides with the quotient metric. We apply some of our results to general stationary axisymmetric spacetime

Real-Time tree foliage estimation using a ground laser scanner

Postprint (published version

First results of a non destructive LIDAR system for the characterisation of tree crops as a support for the optimisation of pesticide treatments

Preprin

Idoneidad y manejo de los datos de un escáner láser (LIDAR) para la caracterización de determinados parámetros vegetativos de interés en frutales y viña

Preprin

Sobre la interfase entre matemáticas y cosmología

Sobre la interfase entre matemáticas y cosmología Carot, Jaume Universidad de Los Andes (ULA) Mérida (Venezuela) Junio de 2004 CONTENIDO Capítulo 1: Algunos Conceptos simples en Geometría Capítulo 2: Transformaciones y Simetrías en general Capítulo 3: El caso de la Cosmología Relativista Capítulo 4: Tópicos [email protected] monográfic

Some developments on axial symmetry

Some developments on axial symmetry (Carot, Jaume) Abstract The definition of axial symmetry in general relativity is reviewed, and some results concerning the geometry in a neighbourhood of the axis are derived. Expressions for the metric are given in different coordinate systems, and emphasis is placed on how the metric coefficients tend to zero when approaching the [email protected] monográfic