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.
Highlights
It is perhaps Lynden-Bell and Nouri-Zonoz [1] who are the first to motivate investigation on the observational possibilities formagnetic monopoles
Abdujabbarov et al [12] discuss some aspects of these geodesics in KTN spacetime, the black hole solution remains a bit in doubt
∓8a M R(R2 − n2) + 2n2 R2 2 − 8n2 R3(a2 + 2n2) = 0. (76). This is the equation to obtain the radius of the inner-most stable circular orbit (ISCO) in nonextremal KTN spacetime for timelike geodesic
Summary
It is perhaps Lynden-Bell and Nouri-Zonoz [1] who are the first to motivate investigation on the observational possibilities for (gravito)magnetic monopoles. There is no specific discussion on the various innermost stable orbits in such spacetimes for null as well as timelike geodesics. This is the gap in the literature which we wish to fill in this paper. In the case of the non-extremal Kerr spacetime Chandrasekhar [14] presents complete and detailed discussion on timelike and null geodesics (including ISCOs and other circular orbits). While centering on the set of ISCOs, we probe the Keplerian orbital frequencies and other important astronomical observables (namely, angular momentum (L), energy (E), rotational velocity (v(φ)) etc.), relevant for accretion disk physics, in the KTN and TaubNUT spacetimes; these have not been investigated extensively in the extant literature.
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