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

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

Automated summary

We establish necessary and sufficient conditions for pseudo-Finsler spaces with (alpha, beta)-metrics to admit a Finsler spacetime structure. This ensures the existence of a Lorentzian signature on a conic subbundle of the tangent bundle and a cone of future-pointing time-like vectors. These identified (alpha, beta)-Finsler spacetimes are potential candidates for applications in gravitational physics. Additionally, we determine the relation between the isometries of an (alpha, beta)-metric and the underlying pseudo-Riemannian metric a, including all (alpha, beta)-metrics that have isometries not shared with a.