Comment on the article "Non-local gravitational corrections in black hole shadow images" by S. O. Alexeyev et al

Recently Alexeyev et al. published paper (J. Theor. Exper. Phys. v. 165, N 4, p. 508 in Russian; arXiv:2404.16079 [gr-qc], the reference is given also in [1]). In the paper the authors discussed an opportunity of estimating spins from the analysis of the shadow reconstruction of black holes, theoretically considered using the nonlocal gravity model proposed earlier for the description of “quantum” black holes. However, in essence, this paper considered circular photon orbits, and the fact that the corresponding motion parameters determine the shape and size of shadows, similarly to Kerr black holes, remained unproven. It is also remained unproven the statement that for an equatorial observer the shadow size in the direction of rotation of quantum black holes remains independent of spin. A long time ago the shadow property was established for the Kerr black hole case.