The Finsler Spacetime Condition for (<i>α</i>,<i>β</i>)-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 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 (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.

Keywords

• Finsler geometry
• (<i>α</i>,<i>β</i>)-metric
• isometry