General electric-magnetic decomposition of fields, positivity and Rainich-like conditions

• J. M. M. Senovilla ^[1]
  1. [1] Universidad del País Vasco/Euskal Herriko Unibertsitatea

     Universidad del País Vasco/Euskal Herriko Unibertsitatea

     Leioa, España

     
• Localización: Proceedings of the XXIII Spanish Relativity Meeting on Reference Frames and Gravitomagnetism: Valladolid, Spain, 6-9 September 2000 / coord. por José Fernando Pascual Sánchez, Luis Floría, Angel San Miguel Blanco, F. Vicente, 2001, ISBN 9810246315, págs. 145-164
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We show how to generalize the classical electric-magnetic decomposition of the Maxwell or the Weyl tensors to arbitrary fields described by tensors of any rank in general n-dimensional spacetimes of Lorentzian signature. The properties and applications of this decomposition are reviewed. In particular, the definition of tensors quadratic in the original fields and with important positivity properties is given. These tensors are usually called "super-energy" (s-e) tensors, they include the traditional energy-momentum, Bel and Bel-Robinson tensors, and satisfy the so-called Dominant Property, which is a straightforward generalization of the classical dominant energy condition satisfied by well-behaved energy-momentum tensors. We prove that, in fact, any tensor satisfying the dominant property can be decomposed as a finite sum of the s-e tensors. Some remarks about the conservation laws derivable from s-e tensors, with some explicit examples, are presented. Finally, we will show how our results can be used to provide adequate generalizations of the Rainich conditions in general dimension and for any physical field.