The Finsler spacetime condition for (α,β)-metrics and their isometries

Abstract

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 that the fundamental tensor has Lorentzian signature on a conic subbundle of the tangent bundle and thus the existence of a cone of future pointing timelike vectors is ensured. The identified (α, β)-Finsler spacetimes are candidates for applications in gravitational physics. Moreover, we completely determine the relation between the isometries of an (α, β)-metric and the isometries of the underlying pseudo-Riemannian metric a; in particular, we list all (α, β)-metrics which admit isometries that are not isometries of a.