  The spacetime properties in the exterior of the Kerr-Newman-NUT-Kiselev black
hole in the Rastall theory of gravity, through particle dynamics are
investigated with the aim to find possible degeneracy of the different black
hole parameters. We show that the effective potential, the energy, and the
angular momentum of a test particle moving in the spacetime of such a black
hole strongly depend on the central black hole parameters. We also evaluate the
innermost stable circular orbit radii of test particles and show how the
spacetime parameters can act on them. Further, we show the results for the
fundamental frequencies of test particles moving at small distances from the
circular orbits in the equatorial plane. We demonstrate that change in the
Rastall parameter $\kappa \lambda$, can make the radial epicyclic frequency to
become zero at larger distances from the central source. We also notice that
for the vertical epicyclic frequencies, in the case of the
Kerr-Newman-NUT-Kiselev black hole in the Rastall theory of gravity lower
frequencies are observed as compared to the frequencies observed in the case of
the Kerr black hole. Finally, we show that for the Kerr-Newman-NUT-Kiselev
black hole in the Rastall gravity, the Keplerian frequencies are almost
identical with the frequencies noticed in the case of the Kerr black hole and
the difference between the two can only be observed in the regions in a very
close vicinity to the central black hole, studied in the present work.

General Relativity and Quantum Cosmology