  The original idea to show the spacetime geometry using few geodesics was
developed by Johnson and Ruffini (1974). We used this idea to interpret the
observational data for rotating BH's. We developed the imitation approach to
simulate a propagation of radiation near BH's. An important problem for this
approach is the diagnostics of a black hole metric using X-ray observational
data of the iron $K_\alpha$-line.
  Observations of Seyfert galaxies in X-ray region reveal the broad emissiion
lines in their spectra, which can arise in inner parts of accretion disks,
where the effects of General Relativity (GR) must be counted. A spectrum of a
solitary emission line (the $K_\alpha$-line of iron, for example) of a hot spot
in Kerr accretion disk is simulated, depending on the radial coordinate $r$ and
the angular momentum $a=J/M$ of a black hole, under the assumption of an
equatorial circular motion of a hot spot. Using results of numerical
simulations it is shown that the characteristic two-peak line profile with the
sharp edges arises at a large distance, (about $r \approx (3-10)r_g$). The
inner regions emit the line, which is observed with one maximum and extremely
broad red wing. High accuracy future spectral observations, being carried out,
could detect the angular momentum $a$ of the black hole. We analyzed the
different parameters of problems on the observable shape of this line and
discussed some possible kinds of these shapes. The total number of geodesics is
about $10^9$ (to simulate possible shapes of the $K_\alpha$-line), so the
number is great enough, especially in comparison with few geodesics in the
original paper by Johnson and Ruffini (1974).
