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

We locally classify all SO(3)-invariant four-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 five classes of non-pseudo-Riemannian (i.e. non-quadratic in the velocities) SO(3)-spherically symmetric pseudo-Finsler Berwald functions, which have either a heavily constrained dependence on the velocities, or, up to a suitable choice of the tangent bundle coordinates, no dependence at all on the time and radial coordinates.

Automated summary

We locally classify all SO(3)-invariant four-dimensional pseudo-Finsler Berwald structures, which are Finslerian geometries closest to (spatially, or SO(3))-spherically symmetric pseudo-Riemannian ones and serve as ansatz to find solutions of Finsler gravity equations that generalize the Einstein equations. We find that there exist five classes of non-pseudo-Riemannian SO(3)-spherically symmetric pseudo-Finsler Berwald functions, which have either a heavily constrained dependence on the velocities or, up to a suitable choice of the tangent bundle coordinates, no dependence at all on the time and radial coordinates.