Palatini approach to Born-Infeld-Einstein theory and a geometric description of electrodynamics

Dan N. Vollick
Phys. Rev. D 69, 064030 – Published 25 March 2004
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Abstract

The field equations associated with the Born-Infeld-Einstein action are derived using the Palatini variational technique. In this approach the metric and connection are varied independently and the Ricci tensor is generally not symmetric. For sufficiently small curvatures the resulting field equations can be divided into two sets. One set, involving the antisymmetric part of the Ricci tensor Rμν, consists of the field equation for a massive vector field. The other set consists of the Einstein field equations with an energy momentum tensor for the vector field plus additional corrections. In a vacuum with Rμν=0 the field equations are shown to be the usual Einstein vacuum equations. This extends the universality of the vacuum Einstein equations, discussed by Ferraris et al., to the Born-Infeld-Einstein action. In the simplest version of the theory there is a single coupling constant and by requiring that the Einstein field equations hold to a good approximation in neutron stars it is shown that mass of the vector field exceeds the lower bound on the mass of the photon. Thus, in this case the vector field cannot represent the electromagnetic field and would describe a new geometrical field. In a more general version in which the symmetric and antisymmetric parts of the Ricci tensor have different coupling constants it is possible to satisfy all of the observational constraints if the antisymmetric coupling is much larger than the symmetric coupling. In this case the antisymmetric part of the Ricci tensor can describe the electromagnetic field.

  • Received 27 September 2003

DOI:https://doi.org/10.1103/PhysRevD.69.064030

©2004 American Physical Society

Authors & Affiliations

Dan N. Vollick

  • Department of Physics and Astronomy and Department of Mathematics and Statistics, Okanagan University College, 3333 College Way, Kelowna, British Columbia, Canada V1V 1V7

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Issue

Vol. 69, Iss. 6 — 15 March 2004

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