Lorentz invariance violation and electromagnetic field in an intrinsically anisotropic spacetime

Abstract

Recently, Kostelecky [V.A. Kostelecky, Phys. Lett. B 701, 137 (2011)] proposed that the spontaneous Lorentz invariance violation (sLIV) is related to Finsler geometry. Finsler spacetime is intrinsically anisotropic and induces naturally Lorentz invariance violation (LIV). In this paper, the electromagnetic field is investigated in locally Minkowski spacetime. The Lagrangian is presented explicitly for the electromagnetic field. It is compatible with the one in the standard model extension (SME). We show the Lorentz--violating Maxwell equations as well as the electromagnetic wave equation. The formal plane wave solution is obtained for the electromagnetic wave. The speed of light may depend on the direction of light and the lightcone may be enlarged or narrowed. The LIV effects could be viewed as influence from an anisotropic media on the electromagnetic wave. In addition, the birefringence of light will not emerge at the leading order in this model. A constraint on the spacetime anisotropy is obtained from observations on gamma--ray bursts (GRBs).

16 pages. One figure and one table are added. One extra section is invoked to constrain the model with GRBs. Version for publiction at the EPJC

References in corpus (8)

• Electrodynamics with Lorentz-violating operators of arbitrary dimension
• Very Special Relativity
• General Very Special Relativity is Finsler Geometry
• Planck-scale modified dispersion relations and Finsler geometry
• Riemann-Finsler geometry and Lorentz-violating kinematics
• Lorentz-violation-induced arrival delays of cosmological particles
• Decoherence induced CPT violation and entangled neutral mesons
• Neutrino superluminality without Cherenkov-like processes in Finslerian special relativity

Cited by in corpus (1)

• Bipartite Riemann-Finsler geometry and Lorentz violation