Finsler spacetime geometry in Physics
arXiv:1903.10185 · doi:10.1142/S0219887819410044
Abstract
Finsler geometry naturally appears in the description of various physical systems. In this review I divide the emergence of Finsler geometry in physics into three categories: as dual description of dispersion relations, as most general geometric clock and as geometry being compatible with the relevant Ehlers-Pirani-Schild axioms. As Finsler geometry is a straightforward generalisation of Riemannian geometry there are many attempts to use it as generalized geometry of spacetime in physics. However, this generalisation is subtle due to the existence of non-trivial null directions. I review how a pseudo-Finsler spacetime geometry can be defined such that it provides a precise notion of causal curves, observers and their measurements as well as a gravitational field equation determining the Finslerian spacetime geometry dynamically. The construction of such Finsler spacetimes lays they foundation for comparing their predictions with observations, in astrophysics as well as in laboratory experiments.
11 pages, submitted to International Journal of Geometric Methods in Modern Physics, match published version
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Cited by in corpus (54)
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- Dark Gravitational Sectors on a Generalized Scalar-Tensor Vector Bundle Model and Cosmological Applications
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- Black Hole Solutions with Constant Ricci Scalar in a Model of Finsler Gravity
- A field theory in Randers-Finsler spacetime
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- Geometric Justification of the Fundamental Interaction Fields for the Classical Long-Range Forces
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- Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
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- Predictions of Ultra-High Energy Cosmic Ray Propagation in the Context of Homogeneously Modified Special Relativity
- Identifying Berwald Finsler Geometries
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- Causal hierarchy in modified gravity
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- Revisiting Legendre transformations in Finsler geometry
- On the significance of the stress-energy tensor in Finsler spacetimes
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- Muon accelerators -- Muon lifetime measurements as window to Planck scale physics
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- Metrizability of SO(3)-invariant connections: Riemann versus Finsler
- From kinetic gases to an exponentially expanding universe - The Finsler-Friedmann equation
- More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques
- A note on Clifford bundles and certain Finsler type spaces
- Electromagnetic and gravitational interactions from Lagrangian mechanics
- Average of geometric structures in Finsler spaces with Lorentzian signature
- Modelling Cosmic Springs with Finsler and Generalised Finsler Geometries
- On Finslerian extension of special relativity
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- Kinetic gases in static spherically symmetric modified dispersion relations
- Experimental Bounds on Deformed Muon Lifetime Dilation