Evaluation of circular orbits and innermost stable circular orbits of neutral and charged particles around black holes

Abstract: In this paper we study the effective gravitational potential of Schwarzschild, Kerr, Reissner-Nordström and Kerr-Newman black holes with the relativistic corrections to evaluate the circular orbits and the Innermost Stable Circular Orbits (ISCOs), a purely relativistic phenomenon, of neutral and charged particles in the vicinity of these spacetimes. We study the circular orbits and ISCOs of black holes mathematically and graphically. Moreover, the astrophysical properties of ISCO are also dealt with. We find that the particle entering the ISCO loses a certain amount of energy, in different spacetimes, by gravitational radiative processes, before finally spiraling into ISCO. The electromagnetic effects of different spacetimes show how the charges sharpen the radius of the circular orbits, and the increasing product of particle and black hole charge increases the radius of the ISCO. Most importantly, the effective potential of the most general spacetime, as predicted by the no-hair conjecture, has been derived.