Bi-metric pseudo-Finslerian spacetimes

Abstract

Finsler spacetimes have become increasingly popular within the theoretical physics community over the last two decades. 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 and/or proof. We shall first provide a few basic definitions, explicitly demonstrating the interpretation of bi-metric theories in terms of pseudo-Finsler norms. We shall then discuss the tricky issues that arise when trying to construct an appropriate pseudo-Finsler metric appropriate to bi-metric spacetimes. Whereas in Euclidian signature the construction of the Finsler metric typically fails at the zero vector, in Lorentzian signature the Finsler metric is typically ill-defined on the entire null cone.

8 pages

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Cited by in corpus (5)

• Classical-physics applications for Finsler $b$ space
• Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles
• 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
• A volume element on time orientable Finslerian spacetimes