Four-dimensional SO(3)-spherically symmetric Berwald Finsler spaces

Abstract

We locally classify all SO(3)-invariant 4-dimensional pseudo-Finsler Berwald structures. These are Finslerian geometries which are closest to (spatially, or SO(3))-spherically symmetric pseudo-Riemannian ones - and serve as ansatz to find solutions of Finsler gravity equations which generalize the Einstein equations. We find that there exist six classes of non pseudo-Riemannian (i.e., non-quadratic in the velocities) SO(3)-spherically symmetric pseudo-Finsler Berwald functions, which have either: a power law, an exponential law, or a one- or two-variable dependence on the velocities.