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.

10 pages; minor changes

References in corpus (3)

• Very Special Relativity
• General Very Special Relativity is Finsler Geometry
• Planck-scale modified dispersion relations and Finsler geometry

Cited by in corpus (6)

• Classical kinematics for isotropic, minimal Lorentz-violating fermion operators
• Redshift in Finsler spacetimes
• Thermodynamics of $f(R)$ Gravity with Disformal Transformation
• Affine sphere spacetimes which satisfy the relativity principle
• On skewon modification of light cone structure
• Finslerian representation of the Maxwell equations