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We consider effects of non-uniformity of quasi-spherical small black holehorizons on scattering massless spineless particles in the long-waveapproximation. Focusing on 4D flat and AdS neutral black hole backgrounds withconformally spherical geometry of the horizon, we observe the notabledifferences in compare to the scattering process on the spherically-symmetricblack holes. In particular, the absorption cross-section becomes dependent onboth, polar and azimuthal, spherical angles, projections of the angularmomentum do not keep anymore and the angular momentum operator by itself,though remains quantised, is not quantised in integers. However, within thelong-wave approximation, the main conclusion of previously obtained results onscattering on the spherically-symmetric black holes remains the same: the totalabsorption cross-section is proportional to the area of the black hole. Theproportionality coefficient does not depend on the scalar wave frequency in theflat space black hole background, and is dependent on the admissible from theunitarity requirement frequencies in the background of AdS black hole. As aby-product of our studies we establish a quasi-spherical non-static Vaidya-typeblack hole solutions and outline the relation between real solutions to theelliptic Liouville equation on 2D plane and on two-dimensional sphere.

Absorption cross-sections of small quasi-spherical black holes: the massless scalar case