Causal structure and electrodynamics on Finsler spacetimes

Details Causal structure and electrodynamics on Finsler spacetimes Causal structure and electrodynamics on Finsler spacetimes

2011-04-06

arxiv.org/abs/1104.1079v2

Phys.Rev.D84:044039,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, 4 figures, additional comments

Scientific paper

10.1103/PhysRevD.84.044039

We present a concise new definition of Finsler spacetimes that generalize Lorentzian metric manifolds and provide consistent backgrounds for physics. Extending standard mathematical constructions known from Finsler spaces we show that geometric objects like the Cartan non-linear connection and its curvature are well-defined almost everywhere on Finsler spacetimes, also on their null structure. This allows us to describe the complete causal structure in terms of timelike and null curves; these are essential to model physical observers and the propagation of light. We prove that the timelike directions form an open convex cone with null boundary as is the case in Lorentzian geometry. Moreover, we develop action integrals for physical field theories on Finsler spacetimes, and tools to deduce the corresponding equations of motion. These are applied to construct a theory of electrodynamics that confirms the claimed propagation of light along Finsler null geodesics.

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