Finsler branes and quantum gravity phenomenology with Lorentz symmetry violations

Abstract

A consistent theory of quantum gravity (QG) at Planck's scale almost surely contains manifestations of Lorentz local symmetry violations (LV) which may be detected at observable scales. This can be effectively described and classified by models with nonlinear dispersions and related Finsler metrics and fundamental geometric objects (nonlinear and linear connections) depending on velocity/momentum variables. We prove that the trapping brane mechanism provides an accurate description of gravitational and matter field phenomena with LV over a wide range of distance scales and recovering in a systematic way the general relativity and local Lorentz symmetries. In contrast to the models with extra spacetime dimensions, the Einstein–Finsler-type gravity theories are positive with nontrivial nonlinear connection structure, nonholonomic constraints and torsion induced by generic off-diagonal coefficients of metrics, and determined by the fundamental QG and/or LV effects.