T. Zannias
Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Apartado Postal 2–82, 58040 Morelia, Mich, MÉXICO e–mail: zannias@ginette.ifm.umich.mx
Recibido el 18 de julio de 2005
Aceptado el 14 de marzo de 2005
Abstract
]]> In this paper, after a brief review of the current observational evidences regarding the phenomenon of cosmic magnetism, we discuss the problems associated with the generation of electromagnetic fields by conducting fluid flows. In particular, we examine the electromagnetic field generated by a conducting fluid flow in the so–called magnetohydrodynamical (MHD) regime in the non–relativistic and general relativistic limit. Our efforts are directed at the status of Cowlings theorem for the two limits. We show that electromagnetic fields generated by conducting fluids in an arbitrary spacetime (M, g) are influenced by the conducting and kinematical variables defining the fluid flow, but also influenced by the curvature and topology of the underlying spacetime. For the particular case of spatially homogeneous and isotropic backgrounds or stationary–axially symmetric circular spacetimes, we show that the dynamical equations describing electromagnetics fields generated by particular conducting flows reduce to a form structurally similar to the non–relativistic limit. Despite this siplification, the issue whether axially symmetric conducting fluid flows can maintain an axisymmetric magnetic field against Ohmic dissipation is still open.Keywords: Magnetohydrodynamics; compact objects; gravitation.
Resumen
En este artículo damos una breve revisión de las evidencias observacionales relacionadas con el fenómeno del magnetismo cósmico. Se discute el problema asociado con la generación de un campo magnético por el flujo de un fluido conductor en el regimen magnetohidrodinámico en el caso no relativista y en relatividad general. El esfuerzo se enfoca en establecer la validez del teorema de Cowling para los dos limites. Los campos electromagnéticos generados por fluidos conductores en un espacio tiempo arbitrario (M, g) son influenciados por las variables de conducción y variables cinemáticas que definen el flujo del fluido, asi como por la curvatura y topología de del espacio tiempo. Para el caso particular de un fondo homogeneo e isotrópico o espacios tiempo estacionarios con simetria axial y circular, se muestra que las ecuaciones dinámicas que describen los campos electromagnéticos generados por flujos conductores se reducen a una forma estructuralmente similar al limite no relativista. Aun asi, queda abierta la cuestión de si flujos de fluidos conductores axial simétricos pueden mantener un campo magnético axialsimétrico a pesar de la disipación ohmica.
Descriptores: Magnetohidrodinámica; objeto compactos; gravitación.
PACS: 04.20–q; 95.30; 95.30.Sf
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]]>Acknowledgments
It is a pleasure to thank U. Nucamendi and in particularl Joaquin Delgado Estevez for many discussions on some of the technical aspects raised in the relativistic treatment. This research was partially supported by a grant from Coordinacion Científica – UMSNH.
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