Dynamics and Fundamental Frequencies of Test Particles Orbiting Kerr-Newman-NUT-Kiselev Blacks Hole in Rastall Gravity

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.