Causal structure and electrodynamics on Finsler spacetimes

Understand

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.