Stationary solutions for the parity-even sector of the CPT-even and Lorentz-covariance-violating term of the standard model extension

Abstract

In this work, we focus on some properties of the parity-even sector of the CPT-even electrodynamics of the standard model extension. We analyze how the six non-birefringent terms belonging to this sector modify the static and stationary classical solutions of the usual Maxwell theory. We observe that the parity-even terms do not couple the electric and magnetic sectors (at least in the stationary regime). The Green's method is used to obtain solutions for the field strengths E and B at first order in the Lorentz- covariance-violating parameters. Explicit solutions are attained for point-like and spatially extended sources, for which a dipolar expansion is achieved. Finally, it is presented an Earth-based experiment that can lead (in principle) to an upper bound on the anisotropic coefficients as stringent as $({\tilde{\kappa }}_{e-}{)}^{ij}<2.9\times 10^{-20}.$

arXiv comment8 pages, revtex style, revised published version, to appear in EPJC (2009)

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