Pseudo-Finslerian spacetimes and multi-refringence

Abstract

It is reasonably well-known that birefringent crystal optics can to some extent be described by the use of pseudo-Finslerian spacetimes (an extension of pseudo-Riemannian spacetime). What is less commonly appreciated is that there are two separate and quite disjoint pseudo-Finsler structures for the two photon polarizations, and further, that there are separate tangent-space pseudo-Finsler structures defined by the group velocity and co-tangent-space pseudo-co-Finsler structures defined by the phase velocity. The inter-connections between these four separate pseudo-Finsler structures are rather subtle. One particular source of technical difficulty is the fact that because physicists need to use pseudo-Finsler structures to describe propagation of signals, there will be nonzero null vectors in both the tangent and cotangent spaces -- this causes significant problems in that many of the mathematical results normally obtained for "usual'' (Euclidean signature) Finsler structures either do not apply, or require significant modifications to their formulation. We shall first provide a few basic definitions, and then present a tutorial outline of the relevant physics of birefringent optics, explicitly demonstrating the interpretation in terms of pseudo-Finsler spacetimes. We shall then discuss the tricky issues that arise when trying to inter-relate the various pseudo-Finsler structures we encounter, and finish by connecting these technical questions (which of course arise in what is a physically a very well-understood situation) back to ongoing research into possible extensions and modifications of general relativity.

V1: 19 pages. V2: Now 30 pages. Title changed, discussion considerably expanded and rearranged, references more than doubled. This version accepted for publication in International Journal of Modern Physics D.

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Cited by in corpus (26)

• Riemann-Finsler geometry and Lorentz-violating kinematics
• Bipartite Riemann-Finsler geometry and Lorentz violation
• Observational constraints on viable f(R) parametrizations with geometrical and dynamical probes
• Resembling dark energy and modified gravity with Finsler-Randers cosmology
• Emergent Models for Gravity: an Overview of Microscopic Models
• Classical-physics applications for Finsler $b$ space
• Modified Dispersion Relations in Horava-Lifshitz Gravity and Finsler Brane Models
• Imperfect fluids, Lorentz violations and Finsler Cosmology
• Cosmological equivalence between the Finsler-Randers space-time and the DGP gravity model
• Finsler-Randers Cosmology: dynamical analysis and growth of matter perturbations
• Covariant kinematics and gravitational bounce in Finsler space-times
• Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions
• Bi-metric pseudo-Finslerian spacetimes
• Birefringence in pseudo-Finsler spacetimes
• Kinematics and dynamics in a Bipartite-Finsler spacetime
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• On Fermat's principle for causal curves in time oriented Finsler spacetimes
• On the analyticity of static solutions of a field equation in Finsler gravity
• Cosmic magnetization in curved and Lorentz violating space-times
• A note on particle kinematics in Horava-Lifshitz scenarios
• On skewon modification of light cone structure
• Causal hierarchy in modified gravity
• The causal structure of spacetime is a parameterized Randers geometry
• Aspects of General Relativity: Pseudo-Finsler extensions, Quasi-normal frequencies and Multiplication of tensorial distributions
• Wind-Finslerian structure of black holes
• On the pseudo-Riemann's quartics in Finsler's geometry