The Finsler spacetime condition for (α,β)-metrics and their isometries
arXiv:2302.09937 · doi:10.3390/universe9040198
Abstract
For the general class of pseudo-Finsler spaces with -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 -Finsler spacetimes are candidates for applications in gravitational physics. Moreover, we completely determine the relation between the isometries of an -metric and the isometries of the underlying pseudo-Riemannian metric ; in particular, we list all -metrics which admit isometries that are not isometries of .
25 pages, Equations (6), (A5) and (A10) have been corrected
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