Finsler-type modification of the Coulomb law

Abstract

Finsler geometry is a natural generalization of pseudo-Riemannian geometry. It can be motivated e.g. by a modified version of the Ehlers-Pirani-Schild axiomatic approach to space-time theory. Also, some scenarios of quantum gravity suggest a modified dispersion relation which could be phrased in terms of Finsler geometry. On a Finslerian spacetime, the Universality of Free Fall is still satisfied but Local Lorentz Invariance is violated in a way not covered by standard Lorentz Invariance Violation schemes. In this paper we consider a Finslerian modification of Maxwell's equations. The corrections to the Coulomb potential and to the hydrogen energy levels are computed. We find that the Finsler metric corrections yield a splitting of the energy levels. Experimental data provide bounds for the Finsler parameters.

arXiv comment10 pages; minor changes

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• Geodesics and the magnitude-redshift relation on cosmologically symmetric Finsler spacetimes
• Classical kinematics for isotropic, minimal Lorentz-violating fermion operators
• Redshift in Finsler spacetimes
• A field theory in Randers-Finsler spacetime
• Thermodynamics of $f(R)$ Gravity with Disformal Transformation
• Affine sphere spacetimes which satisfy the relativity principle
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• On skewon modification of light cone structure
• Photon propagator in skewon electrodynamics
• Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric
• Finslerian representation of the Maxwell equations
• Finslerian geometrodynamics