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

Abstract

For the general class of pseudo-Finsler spaces with $(\hat{I}\pm ,{\hat{I}}^2)$-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 $(\hat{I}\pm ,{\hat{I}}^2)$-Finsler spacetimes are candidates for applications in gravitational physics. Moreover, we completely determine the relation between the isometries of an $(\hat{I}\pm ,{\hat{I}}^2)$-metric and the isometries of the underlying pseudo-Riemannian metric $a$; in particular, we list all $(\hat{I}\pm ,{\hat{I}}^2)$-metrics which admit isometries that are not isometries of $a$.

25 pages, Equations (6), (A5) and (A10) have been corrected