We study a Kerr-like black hole and naked singularity in perfect fluid dark matter (PFDM). The critical value of spin parameter a c is presented to differentiate the black hole from naked singularity. It is seen that for any fixed value of dark matter parameter α the rotating object is black hole if a ≤ a c and naked singularity if a > a c . Also for −2 ≤ α < 2/3 the size of the black hole horizons decrease whereas for 2/3 < α it increases. We also study spin precession frequency of a test gyroscope attached to stationary observer to differentiate a black hole from naked singularity in PFDM. For the black hole, spin precession frequency blows up as the observer reaches the central object while for naked singularity it remains finite except at the ring singularity. Moreover, we study Lense-Thirring precession for a Kerr-like black hole and geodetic precession for Schwarzschild black hole in PFDM. To this end, we have calculated the Kepler frequency (KF), the vertical epicyclic frequency (VEF), and the nodal plane precession frequency (NPPF). Our results show that, the PFDM parameter α significantly affects those frequencies. This difference can be used by astrophysical observations in the near future to shed some light on the nature of dark matter.

Depending on five parameters, rotating counterparts of Einstein-Maxwell-dilaton black holes are derived. We discuss their physical and geometric properties and investigate their null and time-like geodesics including circular orbits. The Lense-Thirring effect is considered.

We study the critical values of the quintessential and spin parameters, to distinguish a rotating Kiselev black hole (RKBH) from a naked singularity. For any value of the dimensionless quintessential parameter ω q ∈ (−1, −1/3), when increasing the value of quintessential parameter α, the size of the event horizon increases, whereas the size of the outer horizon decreases. We then study the spin precession of a test gyroscope attached to a stationary observer in this spacetime. Using the spin precessions we differentiate black holes from naked singularities. If the precession frequency becomes large, as approaching to the central object in the quintessential field along any direction, then the spacetime is a black hole. A spacetime will contain a naked singularity if the precession frequency remains finite everywhere except at the singularity itself. Finally, we study the Lense-Thirring precession frequency for rotating Kiseleb black hole and the geodetic precession for Kiselev black hole.2 of general relativity and to measure the precession rate due to the LT and geodetic effects relative to the Copernican system or the fixed star HR8703, known as IM Pegasi, of a test gyro due to the rotation of the Earth, Gravity Probe B has been launched [29].The geodetic precession in the Schwarzschild black hole and the KBH have been studied in [31][32][33]. The LT-precession in the strong gravitational field of the Kerr and Kerr-Taub-NUT black holes has been discussed in [34].During the gravitational collapse of massive stars, the existence of naked singularities is the topic of great interest for researchers in the field of gravitational theory and relativistic astrophysics. The key question is that how one can differentiate whether the ultimate product in the life cycle of the compact object under the self-gravity collapse is naked singularity or black hole? Mathematically, a black hole is solution of the Einstein field equations (EFE). A stationary vacuum Kerr solution of EFE is characterized by two parameters, namely the mass M and angular momentum J of the central object. If the spin parameter a (angular momentum per unit mass) satisfies the condition M ≥ a, Kerr solution represent black hole and the Kerr singularity is contained in the event horizon. However, if M < a the event horizon disappears, represents the naked singularity. Recently, Chakraborty et al [35,36] gave the criteria based on the spin precession frequency of a test gyroscope attached to both static and stationary observers, to differentiate black holes from naked singularities. Using these criteria the Kerr black hole and naked singularities are discussed.The novelty of the present paper is to differentiate rotating black holes in a quintessential matter (rotating KBH) from a naked singularity. A stationary rotating Kiselev solution of Einstein field equation is characterized by four parameter, black hole mass M, spin parameter a, dimensionless quintessential parameter ω q and quintessential parameter representing the intensity of the quintessence ener...