Foundations of Finsler spacetimes from the Observers' Viewpoint
arXiv:2003.00455 · doi:10.3390/universe6040055
Abstract
Physical foundations for relativistic spacetimes are revisited, in order to check at what extent Finsler spacetimes lie in their framework. Arguments based on inertial observers (as in the foundations of Special Relativity and Classical Mechanics) are shown to correspond with a double linear approximation in the measurement of space and time. While General Relativity appears by dropping the first linearization, Finsler spacetimes appear by dropping the second one. The classical Ehlers-Pirani-Schild approach is carefully discussed and shown to be compatible with the Lorentz-Finsler case. The precise mathematical definition of Finsler spacetime is discussed by using the {\em space of observers}. Special care is taken in some issues such as: the fact that a Lorentz-Finsler metric would be physically measurable only on the causal directions for a cone structure, the implications for models of spacetimes of some apparently innocuous hypotheses on differentiability, or the possibilities of measurement of a varying speed of light.
v2: 47 pages, new section 5.2.5, added seven references and minor changes
References in corpus (8)
- Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
- Very Special Relativity
- Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
- General Very Special Relativity is Finsler Geometry
- Riemann-Finsler geometry and Lorentz-violating kinematics
- Bipartite Riemann-Finsler geometry and Lorentz violation
- Note on Varying Speed of Light Cosmologies
- Relativistic kinetic gases as direct sources of gravity
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- Predictions of Ultra-High Energy Cosmic Ray Propagation in the Context of Homogeneously Modified Special Relativity
- Finsler gravitational waves of -type and their observational signature
- A Cosmological Unicorn Solution to Finsler Gravity
- Anisotropic connections and parallel transport in Finsler spacetimes
- The Finsler spacetime condition for (α,β)-metrics and their isometries
- Cosmological Landsberg Finsler spacetimes
- On the significance of the stress-energy tensor in Finsler spacetimes
- From kinetic gases to an exponentially expanding universe - The Finsler-Friedmann equation
- A variational setting for an indefinite Lagrangian with an affine Noether charge
- Lorentzian-Euclidean black holes and Lorentzian to Riemannian metric transitions
- On Finslerian extension of special relativity
- Electromagnetic and gravitational interactions from Lagrangian mechanics
- Kinetic gases in static spherically symmetric modified dispersion relations