Carlos A. Lopez

Internal structure of a classical spinning electron

A classical model of the spinning electron in general relativity consisting of a rotating charge distribution with Poincaré stresses is set up. It is made out of a continuous superposition of thin charged shells with differential rotation. Each elementary shell is maintained in stationary equilibrium in the gravitational field created by the others. A class of interior solutions of the Kerr-Newman field is thus obtained. The corresponding stress-energy tensor naturally splits into the sum of two terms. The first one is the Maxwell tensor associated to a rotating charge distribution, and the second one corresponds to a material source having zero energy density everywhere, no radial pressure, and an isotropic transverse stress. These negative pressures or tensions are identified with the cohesive forces introduced by Poincaré to stabilize the Lorentz electron model. They are shown to be the source of a negative gravitational mass density and thereby of the violation of the energy conditions inside the electron.

Collapse and rebound of a charged dust-like star

It is shown that a charged spherically symmetric star, made out of a continuous superposition of thin shells with Poincaré stresses, undergoes gravitational collapse in free fall like an uncharged star of dust. The interior solution is a Friedmann universe matching the Reissner-Nordström geometry at the boundary of the star. When the absolute value of the chargeQ does not exceed the massM, the star rebounds elastically inside the event horizon at the radial coordinateQ2/(2M). The further history of the charged star after the bounce is analyzed. Besides, a simple mechanism which accounts for the development of Poincaré stresses in an originally charged star of dust is suggested. It is also verified that the energy density is nonnegative all along the collapse process.

Gravitational Energy from a Quadratic Lagrangian with Torsion

Gravitation is considered as a gauge field within the formalism of Utiyama and Kibble. In empty space-time a Lagrangian density, quadratic in Riemanns curvature tensor and in Cartans torsion tensor, is introduced. The equations of motion are coupled differential equations for the curvature and torsion tensors. The spin of the torsion field behaves as a curvature source and the energy of both fields acts as a torsion source. Each field has an energy tensor, similar to the Maxwell tensor of electrodynamics, vanishing in a torsionless space. It thus appears that the torsion of space-time is a geometric property that makes possible the propagation of gravitational energy in the absence of matter.

Repulsive Gravitation in the Kerr-Newman Field

It is shown that uncharged test particles, released from rest at infinity in the Kerr-Newman field, stop and rebound when the radial coordinate r takes the value r0 = Q2/(2M). This expression corresponds to the position of a stationary source of the Kerr-Newman field found by the author. It represents the surface of a massive oblate ellipsoid of revolution undergoing rigid rotation. Besides, the magnitude of r0 guarantees that no violation of causality occurs throughout spacetime. Although the test particles angular momenta are always zero, they acquire a rotational motion as a consequence of the dragging of inertial frames.

Gravitational collapse in free fall of a slowly rotating star

The Oppenheimer-Snyder model of a spherically symmetric collapse in free fall is generalized to the case in which the star possesses a small rotation. The exterior geometry is chosen to be the Kerr metric in synchronous coordinates, discarding terms of the order (a/r)2. The interior geometry is constructed by adding to the exact metric of the nonrotating case an off-diagonal first-order term in the parametera. This term is determined in part by requiring the validity of the junction conditions at the stars surface and, also, by demanding the conserved angular momentum of the source be equal toMa, in agreement with the value measured by a distant observer. The resulting stress-energy tensor describes a homogeneous, pressureless, ideal fluid (dust) nonuniformly rotating relative to the synchronous frame, which is no longer comoving with the stellar matter. The dynamics of collapse is qualitatively the same as in the spherically symmetric case. Again the stars surface crosses the event horizon when the mass density is finite everywhere, and space-time has not developed any singularity as viewed by freely falling observers at rest in the synchronous frame.

Geometry of rotating charged bubbles in general relativity

It is shown that the spatial geometry of the bubbles with a constant radial coordinatero, embedded in the Kerr-Newman manifold, does not depend on the mass and charge of this solution when referred to a coordinate frame rigidly rotating with the angular velocityω =a(r02+a2)−1. The corresponding line element is found to be identical to the one obtained by Smarr for the surface geometry of a charged rotating black hole.

El tiempo en la física (1)

Se describe el nacimiento del universo a partir dexa0fluctuaciones cuanticas de la nada y se analiza elxa0intervalo de tiempo mas corto imaginable y el masxa0largo conocido. Se analiza tambien el metodo quexa0utilizo Galileo para verificar la caida de los cuerposxa0con una precision increible.

El tiempo en la relatividad

Se describe como la Teoria General de la Relatividad es muy superior a laxa0Teoria de Gravitacion de Newton para el analisis de la cosmologia. Se discutenxa0diversos modelos estaticos de Universo con o sin constante cosmologica y sexa0verifica que ninguno es estable. El problema se resuelve en el ano 1929 conxa0ayuda del telescopio de Monte Wilson en California, demostrando que lasxa0galaxias se alejan unas de otras. Posteriormente, en el ano 1965, se descubre laxa0radiacion de microondas y se discute la posibilidad de que el Universo colapse.