Circular Geodesics in the Kerr-Newman-Taub-NUT Space-time
  In this paper we investigate the equatorial causal (time-like and null) circular geodesics of the Kerr-Newman-Taub-NUT(Newman-Unti-Tamburino) black hole in four dimensional Lorentzian geometry. The special characteristics of this black hole is that it is of \emph{Petrov-Pirani type D} and the photon trajectories are \emph{doubly degenerate principal null congruence}. We derive the conditions for existence of innermost stable circular orbit, marginally bound circular orbit and circular photon orbit in the background of Kerr-Newman-Taub-NUT(KNTN) space-time. The effective potential for both time-like case and null cases have been studied. It is shown that the \emph{presence of the NUT parameter deforms the shape of the effective potential in contrast with the zero NUT parameter}. We further investigate the energy extraction by the Penrose process for this space-time. It is shown that the efficiency of this black hole depends on both the charge and NUT parameter. It is observed that the energy gain is maximum when NUT parameter goes to zero value and for the maximum spin value. When the value of NUT parameter is increasing the energy-gain is decreasing. 
Parthapratim Pradhan
gr-qc math-ph math.MP