The Spectrum of Electromagnetic Jets from Kerr Black Holes and Naked Singularities in the Teukolsky Perturbation Theory
Denitsa R. Staicova, Plamen P. Fiziev
备注：
18 pages, 35 figures, LaTeX file. Final version. Accepted for publication in Astrophysics and Space Science. Amendments. Typos corrected. Novel notion -"primary jet" is introduced. New references and comments added
We give a new theoretical basis for examination of the presence of the Kerr black hole (KBH) or the Kerr naked singularity (KNS) in the central engine of different astrophysical objects around which astrophysical jets are typically formed: X-ray binary systems, gamma ray bursts (GRBs), active galactic nuclei (AGN), etc. Our method is based on the study of the exact solutions of the Teukolsky master equation for electromagnetic perturbations of the Kerr metric. By imposing original boundary conditions on the solutions so that they describe a collimated electromagnetic outflow, we obtain the spectra of possible {\em primary jets} of radiation, introduced here for the first time. The theoretical spectra of primary electromagnetic jets are calculated numerically. Our main result is a detailed description of the qualitative change of the behavior of primary electromagnetic jet frequencies under the transition from the KBH to the KNS, considered here as a bifurcation of the Kerr metric. We show that quite surprisingly the novel spectra describe linearly stable primary electromagnetic jets from both the KBH and the KNS. Numerical investigation of the dependence of these primary jet spectra on the rotation of the Kerr metric is presented and discussed.
This work outlines a fast, high-precision time-domain solver for scalar, electromagnetic and gravitational perturbations on hyperboloidal foliations of Kerr space-times. Time-domain Teukolsky equation solvers have typically used explicit methods, which numerically violate Noether symmetries and are Courant-limited. These restrictions can limit the performance of explicit schemes when simulating long-time extreme mass ratio inspirals, expected to appear in LISA band for 2-5 years. We thus explore symmetric (exponential, Padé or Hermite) integrators, which are unconditionally stable and known to…
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.
Degeneracy in Accretion Disk Spectra from Naked Singularities and Kerr Black Holes: Application to the AGN MCG-06-30-15
PDPIAS, Charusat University（帕迪皮阿斯，查鲁萨特大学）；International Centre for Space and Cosmology, School of Arts and Sciences, Ahmedabad University（国际空间与宇宙学中心，艺术与科学学院，艾哈迈达巴德大学）；Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research（天文与天体物理系，塔塔基础研究所）；MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology（麻省理工学院卡弗里天体物理与空间研究所，麻省理工学院）
We investigate here the issue of observability of high energy collisions around Kerr naked singu- larity and show that the results are in contrast with the Kerr black hole case. We had shown earlier that it would be possible to have ultrahigh energy collisions between the particles close to the loca- tion r = M around the Kerr naked singularity if the Kerr spin parameter transcends the unity by an infinitesimally small amount a $\rightarrow 1^+$. The collision is between initially ingoing particle that turns back as an outgoing particle due to angular momentum barrier, with another ingoing par…
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 collap…
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 $a\leq a_c$ and naked singularity if $a>a_c$. Also for $-2\leqα<2/3$ 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…
We study the properties of black holes and naked singularities by considering stationary observers and light surfaces in Kerr spacetimes. We reconsider the notion of Killing horizons from a special perspective by exploring the entire family of Kerr metrics. To this end, we introduce the concepts of extended plane, Killing throats and bottlenecks for weak (slowly spinning) naked singularities. Killing bottlenecks (or horizon remnants in analogy with the corresponding definition of throats in black holes) are restrictions of the Killing throats appearing in special classes of slowly spinning nak…
We investigate here the particle acceleration by Kerr naked singularities. We consider a collision between particles dropped in from infinity at rest, which follow geodesic motion in the equatorial plane, with their angular momenta in an appropriate finite range of values. When an event horizon is absent, an initially infalling particle turns back as an outgoing particle, when it has the angular momentum in an appropriate range of values, which then collides with infalling particles. When the collision takes place close to what would have been the event horizon in the extremal case, the center…
We perform a detailed analysis of the properties of stationary observers located on the equatorial plane of the ergosphere in a Kerr spacetime, including light-surfaces. This study highlights crucial differences between black hole and the super-spinner sources. In the case of Kerr naked singularities, the results allow us to distinguish between "weak" and "strong" singularities, corresponding to spin values close to or distant from the limiting case of extreme black holes, respectively. We derive important limiting angular frequencies for naked singularities. We especially study very weak sing…
Naked singularities are hypothetical astrophysical objects, characterized by a gravitational singularity without an event horizon. Penrose has proposed a conjecture, according to which there exists a cosmic censor who forbids the occurrence of naked singularities. Distinguishing between astrophysical black holes and naked singularities is a major challenge for present day observational astronomy. A possibility of differentiating naked singularities from black holes is through the comparative study of thin accretion disks properties around rotating naked singularities and Kerr-type black holes,…
We present a detailed analysis of the orbital circular motion of electrically neutral test particles on the equatorial plane of the Kerr-Newman spacetime. Many details of the motion in the cases of black hole and naked singularity sources are pointed out. We identify four different types of orbital regions, which depend on the properties of the orbital angular momentum, and define four different kinds of naked singularities, according to the values of the charge-to-mass ratio of the source. It is shown that the presence of a particular type of counter-rotating test particles is sufficient to u…
The perturbations of the Kerr metric and the miracle of their exact solutions play a critical role in the comparison of predictions of general relativity with astrophysical observations of compact massive objects. The differential equations governing the late-time ring-down of the perturbations of the Kerr metric, the Teukolsky Angular Equation and the Teukolsky Radial Equation, can be solved analytically in terms of confluent Heun functions. In this article, we solve numerically the spectral system formed by those exact solutions and we obtain the electromagnetic (EM) spectra of the Kerr blac…
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 fre…
We analyze the properties of circular orbits of test particles on the equatorial plane of a rotating central mass whose gravitational field is described by the Kerr spacetime. For rotating black holes and naked singularities we explore all the spatial regions where circular orbits can exist and analyze the behavior of the energy and the angular momentum of the corresponding test particles. In particular, we find all the radii at which a test particle can have zero angular momentum due to the repulsive gravity effects generated by naked singularities. We classify all the stability zones of circ…
It is commonly thought that the final product of gravitational collapse is a black hole. Nevertheless, theoretical studies have not yet provided a final answer to the question whether black holes are the only possible outcome or whether naked singularities are also allowed. Observational tests may thus represent a complementary approach. In the present paper, we consider the Janis-Newman-Winicour metric, which describes a rotating source with a surface-like naked singularity. We calculate iron line shapes in the reflection spectrum of a putative disk around a Janis-Newman-Winicour singularity …
Repulsive gravity is a well known characteristic of naked singularities. In this work, we explore light surfaces and find new effects of repulsive gravity. We compare Kerr naked singularities with the corresponding black hole counterparts and find certain structures that are identified as horizon remnants. We argue that these features might be significant for the comprehension of processes that lead to the formation or eventually destruction of black hole Killing horizons. These features can be detected by observing photon orbits, particularly close to the rotation axis, which can be used to d…
The proper understanding of the electromagnetic counterpart of gravity-waves emitters is of serious interest to the multimessenger astronomy. In this article, we study the numerical stability of the quasinormal modes (QNM) and quasibound modes (QBM) obtained as solutions of the Teukolsky Angular Equation and the Teukolsky Radial Equation with appropriate boundary conditions. We use the epsilon-method for the system featuring the confluent Heun functions to study the stability of the spectra with respect to changes in the radial variable. We find that the QNM and QBM are stable in certain regio…
Tilted thin accretion disks in the full Kerr spacetime and their implications
Manipal Centre for Natural Sciences, Manipal Academy of Higher Education（马尼帕尔高等教育局马尼帕尔自然科学中心）；Tata Institute of Fundamental Research（塔塔基础研究所）；MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology（麻省理工学院卡弗里天体物理与空间研究所）
We investigate in detail the circular motion of test particles on the equatorial plane of the ergoregion in the Kerr spacetime. We consider all the regions where circular motion is allowed, and we analyze the stability properties and the energy and angular momentum of the test particles. We show that the structure of the stability regions has definite features that make it possible to distinguish between black holes and naked singularities. The naked singularity case presents a very structured non-connected set of regions of orbital stability, where the presence of counterrotating particles an…
The superradiant scattering of a scalar field with frequency and angular momentum (ω,m) by a near-extreme Kerr black hole with mass and spin (M,J) was derived in the seventies by Starobinsky, Churilov, Press and Teukolsky. In this paper we show that for frequencies scaled to the superradiant bound the full functional dependence on (ω,m,M,J) of the scattering amplitudes is precisely reproduced by a dual two-dimensional conformal field theory in which the black hole corresponds to a specific thermal state and the scalar field to a specific operator. This striking agreement corroborates a conject…
Recently double black hole vacuum and electrovacuum metrics attracted attention as exact solutions suitable for visualization of ultra-compact objects beyond the Kerr paradigm. However, many of the proposed systems are plagued with ring curvature singularities. Here we present a new simple solution of this type which is asymptotically Kerr, has zero electric and magnetic charges, but is endowed with magnetic dipole moment and electric quadrupole moment. It is manifestly free of ring singularities, and contains only a mild string-like singularity on the axis corresponding to a distributional en…
We examine the possibility for the existence of gravitomagnetic monopole ($n_*$) in M87* by using the results obtained from its first Event Horizon Telescope image. By numerically deducing the shadow sizes in Kerr-Taub-NUT (KTN) spacetime, we show that the shadow size increases with increasing $|n_*|$ for a fixed Kerr parameter $|a_*|$ in case of the KTN black hole, whereas for a KTN naked singularity it increases with increasing $n_*$ for a fixed $a_* > 0$ if $n_* > -\cot 17^{\circ}$ . In general, the asymmetry of shadow shape increases if the central dark object in M87 is a KTN/Kerr naked si…
Weak gravitational, electromagnetic, neutrino and scalar fields, considered as perturbations on Kerr background satisfy Teukolsky Master Equation. The two non-trivial equations obtained after separating the variables are the polar angle equation and the radial equation. We solve them by transforming each one into the form of a confluent Heun equation. The transformation depends on a set of parameters, which can be chosen in a such a way, so the resulting equations have simple polynomial solutions for neutrino, electromagnetic, and gravitational perturbations, provided some additional condition…
We study the properties of the relativistic, steady, axisymmetric, low angular momentum, inviscid, advective, geometrically thin accretion flow in a Kerr-Taub-NUT (KTN) spacetime which is characterized by the Kerr parameter ($a_{\rm k}$) and NUT parameter ($n$). Depending on $a_{\rm k}$ and $n$ values, KTN spacetime represents either a black or a naked singularity. We solve the governing equations that describe the relativistic accretion flow in KTN spacetime and obtain all possible global transonic accretion solutions around KTN black hole in terms of the energy $({\cal E})$ and angular momen…
We study the effect caused by external magnetic fields on the observed thermal spectra and iron line profiles of thin accretion discs formed around Kerr black holes and naked singularities. We aim to provide a tool that can be used to estimate the presence of magnetic fields in the neighbourhood of a compact object and to probe the cosmic censorship conjecture in these particular astrophysical environments. We developed a numerical scheme able to calculate thermal spectra of magnetised Page-Thorne accretion discs formed around rotating black holes and naked singularities as seen by an arbitrar…
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 $Ω$, 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 f…
Context. Quasi-periodic variability has been observed in a number of X-ray binaries harboring black hole candidates. In general relativity, black holes are uniquely described by the Kerr metric and, according to the cosmic censorship conjecture, curvature singularities always have to be clothed by an event horizon. Aims. In this paper, we study the effect of an external magnetic field on the observed light curves of orbiting hot spots in thin accretion discs around Kerr black holes and naked singularities. Methods. We employ a ray-tracing algorithm to calculate the light curves and power spect…
