No 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 †

We propose here a specific criterion to address the existence or otherwise of Kerr naked singularities, in terms of the precession of the spin of a test gyroscope due to the frame dragging by the central spinning body. We show that there is indeed an important characteristic difference in the behavior of gyro spin precession frequency in the limit of approach to these compact objects, and this can be used, in principle, to differentiate the naked singularity from black hole. Specifically, if gyroscopes are fixed all along the polar axis upto the horizon of a Kerr black hole, the precession frequency becomes arbitrarily high, blowing up as the event horizon is approached. On the other hand, in the case of naked singularity, this frequency remains always finite and well-behaved. Interestingly, this behavior is intimately related to and is governed by the geometry of the ergoregion in each of these cases which we analyze here. One intriguing behavior that emerges is, in the Kerr naked singularity case, the Lense-Thirring precession frequency (ΩLT) of the gyroscope due to frame-dragging effect decreases as (ΩLT ∝ r) after reaching a maximum, in the limit of r = 0, as opposed to r −3 dependence in all other known astrophysical cases.

The gravitomagnetic monopole is the proposed gravitational analogue of Dirac's magnetic monopole. However, an observational evidence of this aspect of fundamental physics was elusive. Here, we employ a technique involving three primary X-ray observational methods used to measure a black hole spin to search for the gravitomagnetic monopole. These independent methods give significantly different spin values for an accreting black hole. We demonstrate that the inclusion of one extra parameter due to the gravitomagnetic monopole not only makes the spin and other parameter values inferred from the three methods consistent with each other but also makes the inferred black hole mass consistent with an independently measured value. We argue that this first indication of the gravitomagnetic monopole, within our paradigm, is not a result of fine tuning. * Electronic address: chandra@pku.edu.cn † Electronic address: sudip@tifr.res.in