We study here the precession of the spin of a test gyroscope attached to a stationary observer in the Kerr spacetime, specifically, to distinguish a naked singularity (NS) from a black hole (BH). It was shown recently that for gyros attached to static observers, their precession frequency became arbitrarily large in the limit of approach to the ergosurface. For gyros attached to stationary observers that move with nonzero angular velocity $\mathrm{\Omega }$, this divergence at the ergosurface can be avoided. Specifically, for such gyros, the precession frequencies diverge on the event horizon of a BH, but are finite and regular for a NS everywhere except at the singularity itself. Therefore a genuine detection of the event horizon becomes possible in this case. We also show that for a near-extremal NS ($1<a_{*}<1.1$), characteristic features appear in the radial profiles of the precession frequency, using which we can further distinguish a near-extremal NS from a BH, or even from a NS with larger angular momentum. We then investigate the Lense-Thirring (LT) precession or nodal plane precession frequency of the accretion disk around a BH and NS to show that clear distinctions exist for these configurations in terms of radial variation features. The LT precession in equatorial circular orbits increases on approaching a BH, whereas for NS it increases, attains a peak, and then decreases. Interestingly, for $a_{*}=1.089$, it decreases until it vanishes at a certain radius, and it acquires negative values for $a_{*}>1.089$ for a certain range of $r$. For $1<a_{*}<1.089$, a peak appears, but the LT frequency remains positive definite. There are important differences in accretion disk LT frequencies for a BH and a NS and since LT frequencies are intimately related to observed quasiperiodic oscillations, these features might allow us to determine whether a given rotating compact astrophysical object is a BH or a NS.

The Lunar Gravitational-wave Antenna (LGWA) is a proposed array of next-generation inertial sensors to monitor the response of the Moon to gravitational waves (GWs). Given the size of the Moon and the expected noise produced by the lunar seismic background, the LGWA would be able to observe GWs from about 1 mHz to 1 Hz. This would make the LGWA the missing link between space-borne detectors like LISA with peak sensitivities around a few millihertz and proposed future terrestrial detectors like Einstein Telescope or Cosmic Explorer. In this article, we provide a first comprehensive analysis of the LGWA science case including its multi-messenger aspects and lunar science with LGWA data. We also describe the scientific analyses of the Moon required to plan the LGWA mission.

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.

It has recently been proposed that the accreting collapsed object GRO J1655–40 could contain a non-zero gravitomagnetic monopole, and hence could be better described with the more general Kerr-Taub-NUT (KTN) spacetime, instead of the Kerr spacetime. This makes the KTN spacetime astrophysically relevant. In this paper, we study properties of various circular orbits in the KTN spacetime, and find the locations of circular photon orbits (CPOs) and innermost-stable-circular-orbits (ISCOs). Such orbits are important to interpret the observed X-ray spectral and timing properties of accreting collapsed objects, viz., black holes and naked singularities. Here we show that the usual methods to find the ISCO radius do not work for certain cases in the KTN spacetime, and we propose alternate ways. For example, the ISCO equation does not give any positive real radius solution for particular combinations of Kerr and NUT parameter values for KTN naked singularities. In such a case, accretion efficiency generally reaches 100% at a particular orbit of radius r=r₀, and hence we choose r=r₀ as the 'ISCO' for practical purposes.

We study causal geodesics in the equatorial plane of the extremal Kerr–Taub-NUT spacetime, focusing on the inner-most stable circular orbit (ISCO), and we compare its behavior with extant results for the ISCO in the extremal Kerr spacetime. Calculations of the radii of the direct ISCO, its Kepler frequency, and the rotational velocity show that the ISCO coincides with the horizon in the exactly extremal situation. We also study geodesics in the strong non-extremal limit, i.e., in the limit of a 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.