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Register a new userBlack hole-naked singularity dualism and the repulsion of two Kerr black holes due to spin-spin interaction
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We report about the possibility for interacting Kerr sources to exist in two different states - black holes or naked singularities - both states characterized by the same masses and angular momenta. Another surprising discovery reported by us is that in spite of the absence of balance between two Kerr black holes, the latter nevertheless can repel each other, which provides a good opportunity for experimental detection of the spin-spin repulsive force through the observation of astrophysical black-hole binaries.
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We study here the precession of the spin of a test gyroscope attached to a stationary observer in the Kerr spacetime, specifically, to distinguish naked singularity (NS) from 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 non-zero angular velocity $Omega$, 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 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 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 with approach to 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 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 BH and NS and since LT frequencies are intimately related to observed QPOs, these features might allow us to determine whether a given rotating compact astrophysical object is BH or NS.
Motivated by the lack of rotating solutions sourced by matter in General Relativity as well as in modified gravity theories, we extend a recently discovered exact rotating solution of the minimal Einstein-scalar theory to its counterpart in Eddington-inspired Born-Infeld gravity coupled to a Born-Infeld scalar field. This is accomplished with the implementation of a well-developed mapping between solutions of Ricci-Based Palatini theories of gravity and General Relativity. The new solution is parametrized by the scalar charge and the Born-Infeld coupling constant apart from the mass and spin of the compact object. Compared to the spacetime prior to the mapping, we find that the high-energy modifications at the Born-Infeld scale are able to suppress but not remove the curvature divergence of the original naked null singularity. Depending on the sign of the Born-Infeld coupling constant, these modifications may even give rise to an additional timelike singularity exterior to the null one. In spite of that, both of the naked singularities before and after the mapping are capable of casting shadows, and as a consequence of the mapping relation, their shadows turn out to be identical as seen by a distant observer on the equatorial plane. Even though the scalar field induces a certain oblateness to the appearance of the shadow with its left and right endpoints held fixed, the closedness condition for the shadow contour sets a small upper bound on the absolute value of the scalar charge, which leads to observational features of the shadow closely resembling those of a Kerr black hole.
The open question of whether a Kerr black hole can become tidally deformed or not has profound implications for fundamental physics and gravitational-wave astronomy. We consider a Kerr black hole embedded in a weak and slowly varying, but otherwise arbitrary, multipolar tidal environment. By solving the static Teukolsky equation for the gauge-invariant Weyl scalar $psi_0$, and by reconstructing the corresponding metric perturbation in an ingoing radiation gauge, for a general harmonic index $ell$, we compute the linear response of a Kerr black hole to the tidal field. This linear response vanishes identically for a Schwarzschild black hole and for an axisymmetric perturbation of a spinning black hole. For a nonaxisymmetric perturbation of a spinning black hole, however, the linear response does not vanish, and it contributes to the Geroch-Hansen multipole moments of the perturbed Kerr geometry. As an application, we compute explicitly the rotational black hole tidal Love numbers that couple the induced quadrupole moments to the quadrupolar tidal fields, to linear order in the black hole spin, and we introduce the corresponding notion of tidal Love tensor. Finally, we show that those induced quadrupole moments are closely related to the well-known physical phenomenon of tidal torquing of a spinning body interacting with a tidal gravitational environment.
We present results on the mass and spin of the final black hole from mergers of equal mass, spinning black holes. The study extends over a broad range of initial orbital configurations, from direct plunges to quasi-circular inspirals to more energetic orbits (generalizations of Newtonian elliptical orbits). It provides a comprehensive search of those configurations that maximize the final spin of the remnant black hole. We estimate that the final spin can reach a maximum spin $a/M_h approx 0.99pm 0.01$ for extremal black hole mergers. In addition, we find that, as one increases the orbital angular momentum from small values, the mergers produce black holes with mass and spin parameters $lbrace M_h/M, a/M_h rbrace$ ~spiraling around the values $lbrace hat M_h/M, hat a/M_h rbrace$ of a {it golden} black hole. Specifically, $(M_h-hat M_h)/M propto e^{pm B,phi}cos{phi}$ and $(a-hat a)/M_h propto e^{pm C,phi}sin{phi}$, with $phi$ a monotonically growing function of the initial orbital angular momentum. We find that the values of the parameters for the emph{golden} black hole are those of the final black hole obtained from the merger of a binary with the corresponding spinning black holes in a quasi-circular inspiral.
We derive here the orbit equations of particles in naked singularity spacetimes, namely the Bertrand (BST) and Janis-Newman-Winicour (JNW) geometries, and for the Schwarzschild black hole. We plot the orbit equations and find the Perihelion precession of the orbits of particles in the BST and JNW spacetimes and compare these with the Schwarzschild black hole spacetime. We find and discuss different distinguishing properties in the effective potentials and orbits of particle in BST, JNW and Schwarzschild spacetimes, and the particle trajectories are shown for the matching of BST with an external Schwarzschild spacetime. We show that the nature of perihelion precession of orbits in BST and Schwarzschild spacetimes are similar, while in the JNW case the nature of perihelion precession of orbits is opposite to that of the Schwarzschild and BST spacetimes. Other interesting and important features of these orbits are pointed out.
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