Under the null convergence condition and χ_α=0, connected compact totally geodesic null hypersurfaces in Finsler spacetimes have constant surface gravity.
Takano.Introduction to the Theory of Fields in Finsler Spaces, volume Gravitational Measurements, Fundamental Metrology and Constants, De Sabbata, V., Melnikov, V.N
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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.