Inner-most stable circular orbits in extremal and non-extremal Kerr-Taub-NUT spacetimes

TL;DR

This paper analyzes the properties of innermost stable circular orbits (ISCO) in extremal and non-extremal Kerr-Taub-NUT spacetimes, revealing how the ISCO behaves relative to the horizon and NUT charge.

Contribution

It provides a detailed comparison of ISCO characteristics in Kerr-Taub-NUT and Kerr spacetimes, including the effects of NUT charge and extremality on orbit stability.

Findings

ISCO coincides with the horizon in extremal Kerr-Taub-NUT spacetime.

The radius of the ISCO increases with NUT charge in Taub-NUT spacetime.

No stable circular orbits exist in massless NUT spacetimes for timelike geodesics.

Abstract

We study causal geodesics in the equatorial plane of the extremal Kerr-Taub-NUT spacetime, focusing on the Innermost Stable Circular Orbit (ISCO),and compare its behaviour with extant results for the ISCO in the extremal Kerr spacetime. Calculation of the radii of the direct ISCO, its Kepler frequency, and rotational velocity show that the ISCO coincides with the horizon in the exactly extremal situation. We also study geodesics in the strong {\it non}-extremal limit, i.e., in the limit of vanishing Kerr parameter (i.e., for Taub-NUT and massless Taub-NUT spacetimes as special cases of this spacetime). It is shown that the radius of the direct ISCO increases with NUT charge in Taub-NUT spacetime. As a corollary, it is shown that there is no stable circular orbit in massless NUT spacetimes for timelike geodesics.