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Explore the intricate relationship between Finsler Geometry and spacetime regularity in this 39-minute lecture by Miguel Sanchez at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the application of Finsler Geometry in introducing anisotropic modifications to classical relativity and its role as an auxiliary tool for certain standard relativistic spacetimes. Examine various regularity issues arising from this geometry, including the exclusion of Finsler spacetimes by classic Ehlers-Pirani-Schild axioms, different definitions of Lorentz-Finsler metrics and Finsler static or stationary spacetimes, uniqueness of Palatini connections, and topological complications in causal boundary computations. Investigate a specific Riemannian and Finslerian problem related to the conformal boundary, focusing on how improved regularity from C^1 to C^2 enables applications for classic stationary spacetimes and their Finslerian counterparts. Gain insights into cutting-edge research in non-regular spacetime geometry through this comprehensive talk, which was part of the Workshop on "Non-regular Spacetime Geometry" held at the ESI in March 2023.
