The causal structure of black holes, including horizons and interiors, can be encoded in wind-Finsler metrics whose shifted indicatrices track null geodesics.
Kropina metrics and Zermelo navigation on Riemannian manifolds
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The present paper studies globally defined Kropina metrics as solutions of the Zermelo's navigation problem. Moreover, we characterize the Kropina metrics of constant flag curvature showing that up to local isometry, there are only two model spaces of them: the Euclidean space and the odd-dimensional spheres.
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Wind-Finslerian structure of black holes
The causal structure of black holes, including horizons and interiors, can be encoded in wind-Finsler metrics whose shifted indicatrices track null geodesics.