The Finsler Spacetime Condition for (α,β)-Metrics and Their Isometries

For the general class of pseudo-Finsler spaces with (α,β)-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means fundamental tensor has Lorentzian signature on conic subbundle tangent bundle thus existence cone future-pointing time-like vectors is ensured. The identified (α,β)-Finsler spacetimes are candidates for applications in gravitational physics. Moreover, completely determine relation between isometries an (α,β)-metric underlying pseudo-Riemannian metric a; particular, list all (α,β)-metrics which not a.