Static spacetimes with a Finsler angular sector

We consider static spacetimes in spherical coordinates whose angular sector is described by a Finsler metric rather than the standard round metric on the two-dimensional sphere. Our first contribution is kinematical: maintaining arbitrary lapse and radial factors and relying solely on Killing symmetries and the null constraint, we derive model–independent relations for circular photon orbits and the effective dynamics. By specializing the angular sector to a Randers sphere of constant positive flag curvature, we obtain exact expressions for the conserved angular charge and the critical impact parameter, and we quantify a Finslerian Sagnac–type effect. Our second contribution is dynamical: we examine the field equations used in the literature and we revisit the family of hairy black holes in Nekouee et al 2025 Class. Quantum Grav. 42 045002, demonstrating that the analysis therein neglects crucial non-reversible Finsler features. Furthermore, we show that the solutions presented as new reproduce previously known results in Ovalle et al 2021 Phys. Dark Univ. 31 100744.