Deformed relativity symmetries and the local structure of spacetime

Abstract

A spacetime interpretation of deformed relativity symmetry groups was recently proposed by resorting to Finslerian geometries, seen as the outcome of a continuous limit endowed with first order corrections from the quantum gravity regime. In this work we further investigate such connection between deformed algebras and Finslerian geometries by showing that the Finsler geometries associated to the generalisation of the Poincaré group (the so called $\kappa$-Poincaré Hopf algebra) are maximally symmetric spacetimes which are also of the Berwald type: Finslerian spacetimes for which the connections are substantially Riemannian, belonging to the unique class for which the weak equivalence principle still holds. We also extend this analysis by considering a generalization of the de Sitter group (the so called $q$-de Sitter group) and showing that its associated Finslerian geometry reproduces locally the one from the $\kappa$-Poincaré group and that itself can be recast in a Berwald form in an appropriate limit.

20 pages

References in corpus (5)

• Quantum Gravity at a Lifshitz Point
• Planck-scale modified dispersion relations and Finsler geometry
• Realization of DSR-relativistic symmetries in Finsler geometries
• Investigation on Finsler geometry as a generalization to curved spacetime of Planck-scale-deformed relativity in the de Sitter case
• Analogue spacetime based on 2-component Bose-Einstein condensates

Cited by in corpus (17)

• Investigation on Finsler geometry as a generalization to curved spacetime of Planck-scale-deformed relativity in the de Sitter case
• Mathematical foundations for field theories on Finsler spacetimes
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
• Finsler gravitational waves of $(\alpha ,\beta )$-type and their observational signature
• The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Relativistic deformed kinematics: from flat to curved spacetimes
• From Barthel Randers Kropina Geometries to the Accelerating Universe: A Brief Review of Recent Advances in Finslerian Cosmology
• Doubly special relativity as a non-local quantum field theory
• Revisiting Legendre transformations in Finsler geometry
• Exploring black hole mechanics in cotangent bundle geometries
• Metrizability of SO(3)-invariant connections: Riemann versus Finsler
• DSR-relativistic spacetime picture and the phenomenology of Planck-scale-modified time dilation
• Electromagnetic and gravitational interactions from Lagrangian mechanics
• Experimental Bounds on Deformed Muon Lifetime Dilation
• Finslerian geometrodynamics