Techniques of Global analysis applied to gravitation theories: A cosmological black hole?

An elementary model of freely falling observers and emitters within a black hole's radius is examined to determine the redshift spectrum reaching a typical observer. The model is independent of scale, the fundamental unit being the radius (mass) of the black hole. The observers/emitters all follow the same kinds of trajectories: radially inward and starting from rest at spatial infinity. The test-particle role is assumed throughout; i.e., the observers/emitters do not themselves contribute to the gravitational field of the system. By means of redshift formulas and luminosity distance to the emitters, a picture of actual redshifts and blueshifts, with their intensities, emerges for an observer within the black hole's radius. No luminosity distances greater than approximately one-half the radius are considered in this particular study; nevertheless, redshifts and blueshifts up to approximately 0.6 are seen in portions of the observer's celestial sphere. An exotic application can be made, as a curiosity, to a black hole the size of the universe, resulting in a particular anisotropic "cosmology.

Remarks on the Myers-Perry and Einstein Gauss-Bonnet Rotating Solutions

The Kerr-type solutions of the five-dimensional Einstein and Einstein-Gauss-Bonnet equations look pretty similar when written in Kerr-Schild form. However the Myers-Perry spacetime is circular whereas the rotating solution of the Einstein-Gauss-Bonnet theory is not. We explore some consequences of this difference in particular regarding the (non) existence of Boyer-Lindquist-type coordinates and the extension of the manifold

Solution of the vacuum Kerr-Schild problem

The complete solution of the vacuum Kerr-Schild equations in general relativity is presented, including the space-times with a curved background metric. The corresponding result for a flat background has been obtained by Kerr.Comment: 8 page

The Goldberg-Sachs theorem in linearized gravity

The Goldberg-Sachs theorem has been very useful in constructing algebraically special exact solutions of Einstein vacuum equation. Most of the physical meaningful vacuum exact solutions are algebraically special. We show that the Goldberg-Sachs theorem is not true in linearized gravity. This is a remarkable result, which gives light on the understanding of the physical meaning of the linearized solutions.Comment: 6 pages, no figures, LaTeX 2

Linear Einstein equations and Kerr-Schild maps

We prove that given a solution of the Einstein equations $g_{ab}$ for the matter field $T_{ab}$, an autoparallel null vector field $l^{a}$ and a solution $(l_{a}l_{c}, \mathcal{T}_{ac})$ of the linearized Einstein equation on the given background, the Kerr-Schild metric $g_{ac}+\lambda l_{a}l_{c}$ ($\lambda$ arbitrary constant) is an exact solution of the Einstein equation for the energy-momentum tensor $T_{ac}+\lambda \mathcal{T}_{ac}+\lambda ^{2}l_{(a}\mathcal{T}_{c)b}l^{b}$. The mixed form of the Einstein equation for Kerr-Schild metrics with autoparallel null congruence is also linear. Some more technical conditions hold when the null congruence is not autoparallel. These results generalize previous theorems for vacuum due to Xanthopoulos and for flat seed space-time due to G\"{u}rses and G\"{u}rsey.Comment: 9 pages, accepted by Class. Quant. Gra

The Ultrarelativistic Kerr-Geometry and its Energy-Momentum Tensor

The ultrarelativistic limit of the Schwarzschild and the Kerr-geometry together with their respective energy-momentum tensors is derived. The approach is based on tensor-distributions making use of the underlying Kerr-Schild structure, which remains stable under the ultrarelativistic boost.Comment: 16 pages, (AMS-LaTeX), TUW-94-0

General approach to the study of vacuum space-times with an isometry

In vacuum space-times the exterior derivative of a Killing vector field is a 2-form (named here as the Papapetrou field) that satisfies Maxwell's equations without electromagnetic sources. In this paper, using the algebraic structure of the Papapetrou field, we will set up a new formalism for the study of vacuum space-times with an isometry, which is suitable to investigate the connections between the isometry and the Petrov type of the space-time. This approach has some advantages, among them, it leads to a new classification of these space-times and the integrability conditions provide expressions that determine completely the Weyl curvature. These facts make the formalism useful for application to any problem or situation with an isometry and requiring the knowledge of the curvature.Comment: 24 pages, LaTeX2e, IOP style. To appear in Classical and Quantum Gravit

An Iterative Approach to Twisting and Diverging, Type N, Vacuum Einstein Equations: A (Third-Order) Resolution of Stephani's `Paradox'

In 1993, a proof was published, within ``Classical and Quantum Gravity,'' that there are no regular solutions to the {\it linearized} version of the twisting, type-N, vacuum solutions of the Einstein field equations. While this proof is certainly correct, we show that the conclusions drawn from that fact were unwarranted, namely that this irregularity caused such solutions not to be able to truly describe pure gravitational waves. In this article, we resolve the paradox---since such first-order solutions must always have singular lines in space for all sufficiently large values of $r$---by showing that if we perturbatively iterate the solution up to the third order in small quantities, there are acceptable regular solutions. That these solutions become flat before they become non-twisting tells us something interesting concerning the general behavior of solutions describing gravitational radiation from a bounded source.Comment: 11 pages, a plain TeX file, submitted to ``Classical and Quantum Gravity'

La personería en general y la personería como ministerio público

Este trabajo se hace en base al concepto general de lo que es un Personero Municipal y principalmente en su función como MINISTERIO PÚBLICO. Realmente no existe definición jurídica de lo que es el Personero Municipal, solo se alude a él como “Agente del Ministerio Publico”, “Defensor del Pueblo”, “Veedor Ciudadano”, pero que significa verdaderamente “El Personero”, es el que tiene una personería, quien lleva LA VOZ de la comunidad, quien defiende sus intereses, la Personería Municipal es un órgano de vigilancia encargado de vigilar por el cumplimiento de la Constitución , Leyes, Ordenanzas , Acuerdos Y Órdenes Superiores en el Municipio y de vigilar la conducta de los empleados Municipales. Se puede decir entonces que el Personero Municipal es la personificación del control popular en la administración local encargado de velar por el cumplimiento de las normas legales que garantizan los derechos y responsabilidades de la sociedad y del individuo dentro del marco del Municipio. El control a la administración es fundamental ya que la democracia es ante todo un sistema de controles para evitar los abusos del poder, puede apreciarse a magnitud de las responsabilidades de los Personeros y su directa incidencia en el ejercicio de la democracia local. Ya en los albores de renacimiento en los Municipios italianos existía la Institución del SYNDICATUS OFFICIALIUM. Al finalizar su cargo los responsables de la administración ciudadana y los altos funcionarios se sometían por un periodo variable de tiempo al juicio de los administrados. En el caso del Municipio Colombiano el papel del personero siempre ha estado vinculado al control del ejercicio del poder en nombre de los más altos intereses de la sociedad local

Distributional energy momentum tensor of the extended Kerr geometry

We generalize previous work on the energy-momentum tensor-distribution of the Kerr geometry by extending the manifold structure into the negative mass region. Since the extension of the flat part of the Kerr-Schild decomposition from one sheet to the double cover develops a singularity at the branch surface we have to take its non-smoothness into account. It is however possible to find a geometry within the generalized Kerr-Schild class that is in the Colombeau-sense associated to the maximally analytic Kerr-metric.Comment: 12 pages, latex2e, amslatex and epsf macro