A note on circular geodesics in the equatorial plane of an extreme Kerr–Newman black hole

Abstract

We examine the behaviour of circular geodesics describing orbits of neutral test particles around an extreme Kerr–Newman black hole. It is well known that the radial Boyer–Lindquist coordinates of the prograde photon orbit , marginally bound orbit and innermost stable orbit of the extreme Kerr black hole all coincide with the event horizon’s value . We find that for the extreme Kerr–Newman black hole with mass M, angular momentum J and electric charge (), the coordinate equalities , and hold if and only if is greater than or equal to , and , respectively.