Circular Orbits in the Taub-NUT and mass-less Taub-NUT Space-time

TL;DR

This paper investigates the properties of circular geodesics in Taub-NUT and mass-less Taub-NUT spacetimes, highlighting the influence of the NUT parameter on geodesic structure, and analyzes the radii of key orbits and energy in these spacetimes.

Contribution

It provides a detailed comparison of geodesic structures between Taub-NUT and mass-less Taub-NUT spacetimes, including the computation of orbit radii and center-of-mass energy, revealing unique features of extreme NUT black holes.

Findings

NUT parameter significantly alters the potential well shape.

ISCO, MBCO, and CPO radii coincide with the horizon in extreme TN black holes.

Center-of-mass energy remains finite for non-extreme cases, diverging in extreme NUT black holes.

Abstract

In this work we study the equatorial causal geodesics of the Taub-NUT (TN) space-time in comparison with \emph{mass-less} TN space-time. We emphasized both on the null circular geodesics and time-like circular geodesics. From the effective potential diagram of null and time-like geodesics, we differentiate the geodesics structure between TN spacetime and mass-less TN space-time. It has been shown that there is a key role of the NUT parameter to changes the shape of pattern of the potential well in the NUT spacetime in comparison with \emph{mass-less} NUT space-time. We compared the ISCO (innermost stable circular orbit), MBCO (marginally bound circular orbit) and CPO (circular photon orbit) of the said space-time with graphically in comparison with mass-less cases. Moreover, we compute the radius of ISCO, MBCO and CPO for \emph{extreme} TN black hole (BH). Interestingly, we show that these \emph{three radii} coincides with the Killing horizon i.e. the null geodesic generators of the horizon. Finally in Appendix-A, we compute the center-of-mass (CM) energy for TN BH and mass-less TN BH. We show that in both cases the CM energy is finite. For \emph{extreme} NUT BH, we have found that the diverging nature of CM energy. \emph{First}, we have observed that a non-asymptotic flat, spherically symmetric and stationary extreme BH is showing such feature.