Abstract: |
Finsler geometry has been used to construct spacetimes beyond general relativity, but it also emerges in certain spatial geometries within general relativity. In this talk, I will begin by reviewing the spatial Riemann-Finsler optical geometry for null geodesics of stationary Lorentzian spacetimes, and the extension to Jacobi-Maupertuis metrics for massive particles. In particular, I will describe various approaches of the Gauss-Bonnet method which have been applied in this context. Then I will discuss how Penrose's plane wave limit about null geodesics of any Lorentzian spacetime may be extended to a Lorentz-Finsler setting, by constructing suitable null coordinates and a notion of Finsler pp-waves, showing how the argument can be modelled closely on the corresponding Lorentzian results of general relativity. This includes some joint work with Gary Gibbons (Cambridge), Amir Aazami (Clark, previously IPMU) and Miguel Angel Javaloyes (Murcia). |