Abstract
The black-hole horizon of the Kiselev spacetime, supported by a Kiselev-type anisotropic matter source, is studied within lightlike hypersurface geometry. After separating the two-horizon, degenerate-horizon, and horizonless parameter regimes, we focus on the non-extremal black-hole branch. Ingoing Eddington–Finkelstein coordinates give a regular chart, and the radical and lightlike transversal bundles, induced connection, second fundamental forms, shape operators, and connection 1-form are calculated for the natural SO(3)-adapted screen. We obtain [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. Hence the horizon is totally geodesic, irrotational, minimal, and screen totally umbilical, but not screen conformal relative to the chosen screen. Its generators have zero expansion, shear, and twist, and the screen cross-sections are round spheres. For the static Killing normalization, [Formula: see text]. Increasing [Formula: see text] enlarges the black-hole horizon while lowering its surface gravity and Hawking temperature; a dimensionally consistent increase of [Formula: see text] yields the opposite behavior. In the degenerate limit, the temperature tends to zero and the parameter-response coefficients become singular.