Do compact objects bend space in ways Einstein's equations can't capture?

General relativity assumes spacetime geometry is Riemannian, but Finsler geometry relaxes that constraint. Solving the Finsler gravity vacuum equations under spherical symmetry and asymptotic flatness — conditions any realistic isolated star must satisfy — yields three new families of exact solutions that are not Ricci flat, meaning they differ from anything general relativity can produce. These are the first non-trivial exact spherically symmetric vacuum solutions in the theory, offering concrete candidates for testing whether gravity around compact objects has structure beyond Einstein.