Strong gravity Lense–Thirring precession in Kerr and Kerr–Taub–NUT spacetimes

Abstract

An exact expression derived in the literature for the rate of dragging of inertial frames (Lense-Thirring (LT) precession) in a general stationary spacetime, is reviewed. The exact LT precession frequencies for Kerr, Kerr-Taub-NUT and Taub-NUT spacetimes are explicitly derived. Remarkably, in the case of the zero angular momentum Taub-NUT spacetime, the frame-dragging effect is shown not to vanish, when considered for spinning test gyroscopes. The result becomes sharper for the case of vanishing ADM mass of that spacetime. We clarify how our results are consistent with claims in the recent literature of null orbital plane precession for NUT spacetimes. * chandrachur.chakraborty@saha.ac.in †

Distinguishing Kerr naked singularities and black holes using the spin precession of a test gyro in strong gravitational fields

“…(4), Ω s becomes Ω LT , the Lense-Thirring (LT) precession frequency. This can be expressed as [2,10],…”

“…[2] where the exact Lense-Thirring (LT) precession frequency of a test gyroscope in Kerr spacetime has been derived and it was shown that the LT precession frequency diverges on the boundary of the ergoregion (henceforth, 'ergosurface') of a BH. For BHs, the dimensionless Kerr parameter satisfies a * = J/M 2 ≤ 1.…”

Center of mass energy of the collision for two general geodesic particles around a Kerr-Newman-Taub-NUT black hole

“…In [17], the authors studied the collision for two particles with different rest masses moving in the equatorial plane of a Kerr-Taub-NUT black hole. They demonstrated that the CME depends on the spin parameter a and NUT (Newman-Unti-Tamburino) charge n. Exact Lense-Thirring (LT) precession and causal geodesics in the inner-most stable circular orbit (ISCO) in a KerrTaub-NUT black hole was studied in [18][19][20]. The CME of the collision for two uncharged particles falling freely from rest at infinity in the background of a charged, rotating and accelerating black hole was investigated in [21].…”

“…The conditions for the allowed region, R(r) ≥ 0 and Θ(θ) ≥ 0 give 19) where K (2) min and K (2) max are given by The inequality (3.19) gives the upper and lower bounds for the Carter constant K. By eq. (3.19), one can say that the marginally bound particle with the critical angular momentum reaches the inner horizon of the non-extremal KNTN black hole if the following condition is satisfied 22) where…”

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

“…E.g., while it has been demonstrated in Ref. [2] that the orbital precession of spinless test particles in Taub-NUT geodesics vanishes, investigation by P. Majumdar and me has shown that in both the massive and massless Taub-NUT spacetimes spinning gyroscopes exhibit non-trivial frame-dragging (Lense-Thirring) precession [15]. Even though we do not discuss inertial framedragging in detail in this paper, this does provide a theoretical motivation as well to probe ISCOs in KTN spacetimes, following well-established techniques [14].…”