Lorentz invariance violation and electromagnetic field in an intrinsically anisotropic spacetime

TL;DR

This paper explores how Lorentz invariance violation, arising from Finsler geometry's anisotropic spacetime, affects electromagnetic fields, leading to direction-dependent light speed and potential observational constraints.

Contribution

It presents a Lorentz-violating electromagnetic theory in Finsler spacetime, deriving Maxwell equations and wave solutions consistent with the standard model extension.

Findings

Light speed depends on propagation direction.

No leading-order birefringence observed.

Constraints on spacetime anisotropy from gamma-ray burst data.

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).