Finsler Branes and Quantum Gravity Phenomenology with Lorentz Symmetry Violations

TL;DR

This paper explores Finsler geometry models to describe quantum gravity effects and Lorentz symmetry violations, providing a framework that recovers general relativity at observable scales.

Contribution

It introduces Einstein-Finsler gravity theories with nonlinear connections and torsion, systematically modeling Lorentz violations in quantum gravity scenarios.

Findings

Finsler metrics effectively describe Lorentz symmetry violations.

The trapping brane mechanism models gravitational phenomena with LV.

Theories recover general relativity at large scales.

Abstract

A consistent theory of quantum gravity (QG) at Planck scale almost sure 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 (GR) and local Lorentz symmetries. In contrast to the models with extra spacetime dimensions, the Einstein-Finsler type gravity theories are positively with nontrivial nonlinear connection structure, nonholonomic constraints and torsion induced by generic off-diagonal coefficients of metrics, and determined by fundamental QG and/or LV effects.