Under the null convergence condition and χ_α=0, connected compact totally geodesic null hypersurfaces in Finsler spacetimes have constant surface gravity.
Rademacher.Nonreversible Finsler metrics of positive flag curvature, volume A sampler of Riemann-Finsler geometry, volume 50 of Math
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Totally geodesic null hypersurfaces and constancy of surface gravity in Finsler spacetimes
Under the null convergence condition and χ_α=0, connected compact totally geodesic null hypersurfaces in Finsler spacetimes have constant surface gravity.