Extreme Kerr Black Hole Research Articles

EVOLUTIONS OF STELLAR-MASS BLACK HOLE HYPERACCRETION SYSTEMS IN THE CENTER OF GAMMA-RAY BURSTS

A neutrino-dominated accretion disk around a stellar-mass black hole (BH) can power a gamma-ray burst (GRB) via annihilation of neutrinos launched from the disk. For the BH hyperaccretion system, high accretion rate should trigger the violent evolution of the BH's characteristics, which further leads to the evolution of the neutrino annihilation luminosity. In this paper, we consider the evolution of the accretion system to analyze the mean time-dependent neutrino annihilation luminosity with the different mean accretion rates and initial BH parameters. By time-integrating the luminosity, the total neutrino annihilation energy with the reasonable initial disk mass can satisfy the most of short-duration GRBs and about half of long-duration GRBs. Moreover, the extreme Kerr BH should exist in the cental engines of some high-luminosity GRBs. GRBs with higher energy have to request the alternative magnetohydrodynamics processes in the centers, such as the Blandford-Znajek jet from the accretion system or the millisecond magnetar.

Kerr black holes with self-interacting scalar hair: Hairier but not heavier

The maximal ADM mass for (mini-)boson stars (BSs) -- gravitating solitons of Einstein's gravity minimally coupled to a free, complex, mass $\mu$, Klein-Gordon field -- is $M_{\rm ADM}^{\rm max}\sim M_{Pl}^2/\mu$. Adding quartic self-interactions to the scalar field theory, described by the Lagrangian $\mathcal{L}_I=\lambda |\Psi|^4$, the maximal ADM mass becomes $M_{\rm ADM}^{\rm max}\sim \sqrt{\lambda}M_{Pl}^3/\mu^2$. Thus, for mini-BSs, astrophysically interesting masses require ultra-light scalar fields, whereas self-interacting BSs can reach such values for bosonic particles with Standard Model range masses. We investigate how these same self-interactions affect Kerr black holes with scalar hair (KBHsSH) [1], which can be regarded as (spinning) BSs in stationary equilibrium with a central horizon. Remarkably, whereas the ADM mass scales in the same way as for BSs, the \textit{horizon mass} $M_H$ does not increases with the coupling $\lambda$, and, for fixed $\mu$, it is maximized at the "Hod point", corresponding to the extremal Kerr black hole obtained in the vanishing hair limit. This mass is always $M_{\rm H}^{\rm max }\sim M_{\rm Pl}^2/\mu$. Thus, introducing these self-interactions, the black hole spacetimes may become considerably "hairier" but the trapped regions cannot become "heavier". We present evidence this observation also holds in a model with $\mathcal{L}_I= \beta|\Psi|^6-\lambda|\Psi|^4$; if it extends to \textit{general} scalar field models, KBHsSH with astrophysically interesting horizon masses \textit{require} ultra-light scalar fields. Their existence, therefore, would be a smoking gun for such (beyond the Standard Model) particles.

How fast can a black hole rotate?

Kerr black holes (BHs) have their angular momentum, [Formula: see text], bounded by their mass, [Formula: see text]: [Formula: see text]. There are, however, known BH solutions violating this Kerr bound. We propose a very simple universal bound on the rotation, rather than on the angular momentum, of four-dimensional, stationary and axisymmetric, asymptotically flat BHs, given in terms of an appropriately defined horizon linear velocity, [Formula: see text]. The [Formula: see text] bound is simply that [Formula: see text] cannot exceed the velocity of light. We verify the [Formula: see text] bound for known BH solutions, including some that violate the Kerr bound, and conjecture that only extremal Kerr BHs saturate the [Formula: see text] bound.

Bifurcation of the quasinormal spectrum and zero damped modes for rotating dilatonic black holes

It has been recently found that for the near extremal Kerr black holes appearing of Zero Damped Modes (accompanied by qusinormal mode branching) signifies about inapplicability of the regime of small perturbations and the onset of turbulence. Here we show that this phenomena is not limited by Kerr or Kerr-Newman solutions only, but also takes place for rotating dilatonic black holes for which we have found Zero Damped Modes both numerically and analytically. We have also shown that, contrary to recent claims, there is no instability of a charged massive scalar field in the background of the rotating dilatonic black hole under physically adequate boundary conditions. Analytic expression for dominant quasinormal frequencies is deduced in the regime of large coupling qQ, where q and Q are the field and black hole charges respectively.

Rotating Hayward’s regular black hole as particle accelerator

Recently, Bañados, Silk and West (BSW) demonstrated that the extremal Kerr black hole can act as a particle accelerator with arbitrarily high center-of-mass energy (ECM) when the collision takes place near the horizon. The rotating Hayward’s regular black hole, apart from Mass (M) and angular momentum (a), has a new parameter g (g > 0 is a constant) that provides a deviation from the Kerr black hole. We demonstrate that for each g, with M = 1, there exist critical a E and r , which corresponds to a regular extremal black hole with degenerate horizons, and a E decreases whereas r increases with increase in g. While a < a E describe a regular non-extremal black hole with outer and inner horizons. We apply the BSW process to the rotating Hayward’s regular black hole, for different g, and demonstrate numerically that the ECM diverges in the vicinity of the horizon for the extremal cases thereby suggesting that a rotating regular black hole can also act as a particle accelerator and thus in turn provide a suitable framework for Plank-scale physics. For a non-extremal case, there always exist a finite upper bound for the ECM, which increases with the deviation parameter g.

A note on circular geodesics in the equatorial plane of an extreme Kerr–Newman black hole

We examine the behaviour of circular geodesics describing orbits of neutral test particles around an extreme Kerr–Newman black hole. It is well known that the radial Boyer–Lindquist coordinates of the prograde photon orbit , marginally bound orbit and innermost stable orbit of the extreme Kerr black hole all coincide with the event horizon’s value . We find that for the extreme Kerr–Newman black hole with mass M, angular momentum J and electric charge (), the coordinate equalities , and hold if and only if is greater than or equal to , and , respectively.

Exact solutions for extreme black hole magnetospheres

We present new exact solutions of Force-Free Electrodynamics (FFE) in the Near-Horizon region of an Extremal Kerr black hole (NHEK) and offer a complete classification of the subset that form highest-weight representations of the spacetime's SL(2,R) x U(1) isometry group. For a natural choice of spacetime embedding of this isometry group, the SL(2,R) highest-weight conditions lead to stationary solutions with non-trivial angular dependence, as well as axisymmetry when the U(1)-charge vanishes. In addition, we unveil a hidden SL(2,C) symmetry of the equations of FFE that stems from the action of a complex automorphism group, and enables us to generate an SL(2,C) family of (generically time-dependent) solutions. We then obtain still more general solutions with less symmetry by appealing to a principle of linear superposition that holds for solutions with collinear currents and allows us to resum the highest-weight primaries and their SL(2,R)-descendants.

Scalar fields and particle accelerators

The phenomenon discovered in 2009 by Ba\~nados, Silk and West where particle collisions can achieve arbitrary high center-of-mass (c.m.) energies close to the event horizon of an extreme Kerr black hole, has generated a lot of interest. Although rotation seemed to be an essential requirement, it was later shown that arbitrary high energies can also be achieved for collisions between radially moving particles near the horizon of the electrically charged extreme Reissner-Nordstr\om black hole. Recently Patil and Joshi claimed that instead of spinning up the black hole one can also crank up the c.m. energy of particle collisions by ``charging up'' a static black hole with a massless scalar field. In this regard they showed that infinite energies can be attained in the vicinity of the naked singularity of the Janis-Newman-Wincour (JNW) spacetime, which contains a massless scalar field that also becomes infinite at the position of the curvature singularity. In this study we show that Patil and Joshi's claim does not apply for other static black hole systems endowed with a massless scalar field. In particular we consider the well-known Bekenstein black hole and the recently discovered Mart\'{\i}nez-Troncoso-Zanelli black hole, and show that the expression of the c.m. energy for particle collisions near the event horizons of these black holes is no different than the corresponding case with vanishing scalar field represented by the Schwarzschild solution. Moreover by studying the motion of scalar test charges that interact with the background scalar field in these black hole spacetimes we show that the resulting c.m. energies are even smaller than in the case of free particles. This shows that the infinite energies obtained by Patil and Joshi may not be due to the fact that the black hole contains a massless scalar field, but may be instead related to the geometry of the naked singularity in the JNW spacetime. An analogous case of infinite c.m. energy in the vicinity of a naked singularity is also presented.

Innermost stable circular orbits of spinning test particles in Schwarzschild and Kerr space-times

We consider the motion of classical spinning test particles in Schwarzschild and Kerr metrics and investigate innermost stable circular orbits (ISCO). The main goal of this work is to find analytically the small-spin corrections for the parameters of ISCO (radius, total angular momentum, energy, orbital angular frequency) of spinning test particles in the case of vectors of black hole spin, particle spin and orbital angular momentum being collinear to each other. We analytically derive the small-spin linear corrections for arbitrary Kerr parameter $a$. The cases of Schwarzschild, slowly rotating and extreme Kerr black hole are considered in detail. For a slowly rotating black hole, the ISCO parameters are obtained up to quadratic in $a$ and particle's spin $s$ terms. From the formulas obtained it is seen that the spin-orbital coupling has attractive character when spin and angular momentum are parallel and repulsive when they are antiparallel. For the case of the extreme Kerr black hole with co-rotating particle we succeed to find the exact analytical solution for the limiting ISCO parameters for arbitrary spin. It has been shown that the limiting values of ISCO radius and frequency do not depend on the particle's spin while values of energy and total angular momentum depend on it. We have also considered circular orbits of arbitrary radius and have found small-spin linear corrections for the total angular momentum, energy and frequency at given radius. System of equations for numerical calculation of ISCO parameters for arbitrary $a$ and $s$ is also explicitly written.

Bounds for axially symmetric linear perturbations for the extreme Kerr black hole

We obtain remarkably simple integral bounds for axially symmetric linear perturbations for the extreme Kerr black hole in terms of conserved energies. From these estimates we deduce pointwise bounds for the perturbations outside the horizon.

Timescale for trans-Planckian collisions in Kerr spacetime

We make a critical comparison between ultra-high–energy particle collisions around an extremal Kerr black hole and that around an over-spinning Kerr singularity, mainly focusing on the issue of the timescale of collisions. We show that the time required for two massive particles with the proton mass or two massless particles of GeV energies to collide around the Kerr black hole with Planck energy is several orders of magnitude longer than the age of the Universe for astro-physically relevant masses of black holes, whereas time required in the over-spinning case is of the order of ten million years, which is much shorter than the age of the Universe. Thus, from the point of view of observation of Planck scale collisions, the over-spinning Kerr geometry, subject to their occurrence, has distinct advantage over their black-hole counterparts.

Particle motion and Penrose processes around rotating regular black hole

The neutral particle motion around rotating regular black hole that was derived from the Ayón-Beato-García (ABG) black hole solution by the Newman-Janis algorithm in the preceding paper (Toshmatov et al., Phys. Rev. D, 89:104017, 2014) has been studied. The dependencies of the ISCO (innermost stable circular orbits along geodesics) and unstable orbits on the value of the electric charge of the rotating regular black hole have been shown. Energy extraction from the rotating regular black hole through various processes has been examined. We have found expression of the center of mass energy for the colliding neutral particles coming from infinity, based on the BSW (Baňados-Silk-West) mechanism. The electric charge Q of rotating regular black hole decreases the potential of the gravitational field as compared to the Kerr black hole and the particles demonstrate less bound energy at the circular geodesics. This causes an increase of efficiency of the energy extraction through BSW process in the presence of the electric charge Q from rotating regular black hole. Furthermore, we have studied the particle emission due to the BSW effect assuming that two neutral particles collide near the horizon of the rotating regular extremal black hole and produce another two particles. We have shown that efficiency of the energy extraction is less than the value 146.6 % being valid for the Kerr black hole. It has been also demonstrated that the efficiency of the energy extraction from the rotating regular black hole via the Penrose process decreases with the increase of the electric charge Q and is smaller in comparison to 20.7 % which is the value for the extreme Kerr black hole with the specific angular momentum a=M.

On neutral scalar radiation by a massive orbiting star in extremal Kerr-Newman black hole

We extend the work of 1401.3746 about gravitational waves by a massive orbiting star in an extremal Kerr black hole to an extremal Kerr-Newman black hole for the scalar radiation, and we still find that it has a CFT interpretation from Kerr-Newman/CFT, because our scalar is neutral although the black hole is a charged one. When the charge of black hole is zero, we can get the result of 1401.3746, so we give a new evidence on Kerr-Newman/CFT. In addition, we investigate on electromagnetic radiation with Kerr/CFT in detail which isn't given by 1401.3746.

Stability of event horizons against neutrino flux: the classical picture

It has been claimed that cosmic censorship conjecture (CCC) can be violated by quantum tunnelling of neutrinos, though it is strongly supported by classical arguments. We consider the classical interaction of an extremal Kerr black hole with a test massless Dirac field, i.e. a ‘neutrino field’. Evaluating the flux integrals imposed by the energy momentum tensor for fermionic fields and the Killing vectors of the space–time, we prove that this interaction can indeed destroy the event horizon of the black hole and convert it to a naked singularity. The classical process leads to a more generic violation of CCC compared to quantum tunnelling processes which occur with a low probability. The range of frequencies of the test neutrino field that can be used to destroy the black hole turns out to be the superradiant range for bosonic fields. We comment on back reaction and quantum effects. We argue that the destruction of black holes by neutrino fields cannot be fixed by self-force effects unlike similar attempts involving test bodies and bosonic fields.

Nearly extremal apparent horizons in simulations of merging black holes

The spin angular momentum S of an isolated Kerr black hole is bounded by the surface area A of its apparent horizon: , with equality for extremal black holes. In this paper, we explore the extremality of individual and common apparent horizons for merging, rapidly spinning binary black holes. We consider simulations of merging black holes with equal masses M and initial spin angular momenta aligned with the orbital angular momentum, including new simulations with spin magnitudes up to . We measure the area and (using approximate Killing vectors) the spin on the individual and common apparent horizons, finding that the inequality is satisfied in all cases but is very close to equality on the common apparent horizon at the instant it first appears. We also evaluate the Booth–Fairhurst extremality, whose value for a given apparent horizon depends on the scaling of the horizon’s null normal vectors. In particular, we introduce a gauge-invariant lower bound on the extremality by computing the smallest value that Booth and Fairhurst’s extremality parameter can take for any scaling. Using this lower bound, we conclude that the common horizons are at least moderately close to extremal just after they appear. Finally, following Lovelace et al (2008 Phys. Rev. D 78 084017), we construct quasiequilibrium binary-black hole initial data with ‘overspun’ marginally trapped surfaces with . We show that the overspun surfaces are indeed superextremal: our lower bound on their Booth–Fairhurst extremality exceeds unity. However, we confirm that these superextremal surfaces are always surrounded by marginally outer trapped surfaces (i.e., by apparent horizons) with . The extremality lower bound on the enclosing apparent horizon is always less than unity but can exceed the value for an extremal Kerr black hole.

A holographic bound on the total number of computations in the visible universe

Information I in holographic imaging of massive particles by star-like screens is shown to represent the probability of detection based on their propagator. Results are derived for screens in the shape of a plane, cube and sphere from unitarity in the exponentially small transition probability for a detection outside. We derive I = 2πΔφ in log 2 bits for the imaging of a particle by a spherical screen at a relative de Broglie phase Δφ. Encoding mass, charge, angular momentum or radiation requires at minimum four bits. Minimal screens at maximal information density hereby recover Reissner–Nordström and extremal Kerr black holes. Applied to the visible Universe, the Hubble flow of galaxies through the cosmological event horizon leaves 10121 computations in the future.

Revised upper limit to energy extraction from a Kerr black hole.

We present a new upper limit on the energy that may be extracted from a Kerr black hole by means of particle collisions in the ergosphere (i.e., the "collisional Penrose process"). Earlier work on this subject has focused largely on particles with critical values of angular momentum falling into an extremal Kerr black hole from infinity and colliding just outside the horizon. While these collisions are able to reach arbitrarily high center-of-mass energies, it is very difficult for the reaction products to escape back to infinity, effectively limiting the peak efficiency of such a process to roughly 130%. When we allow one of the initial particles to have impact parameter b>2M, and thus not get captured by the horizon, it is able to collide along outgoing trajectories, greatly increasing the chance that the products can escape. For equal-mass particles annihilating to photons, we find a greatly increased peak energy of Eout≈6×Ein. For Compton scattering, the efficiency can go even higher, with Eout≈14×Ein, and for repeated scattering events, photons can both be produced and escape to infinity with Planck-scale energies.

Force-free electrodynamics around extreme Kerr black holes

Plasma-filled magnetospheres can extract energy from a spinning black hole and provide the power source for a variety of observed astrophysical phenomena. These magnetospheres are described by the highly nonlinear equations of force-free electrodynamics, or FFE. Typically these equations can only be solved numerically. In this paper we consider the FFE equations very near the horizon of a maximally spinning black hole, where the energy extraction takes place. Thanks to an enhanced conformal symmetry which appears in this near-horizon region, we are able to analytically obtain several infinite families of exact solutions of the full nonlinear equations.

Super-spinning compact objects and models of high-frequency quasi-periodic oscillations observed in Galactic microquasars

We have previously applied several models of high-frequency quasi-periodic oscillations (HF QPOs) to estimate the spin of the central Kerr black hole in the three Galactic microquasars, GRS 1915+105, GRO J1655-40, and XTE J1550-564. Here we explore the alternative possibility that the central compact body is a super-spinning object (or a naked singularity) with the external space-time described by Kerr geometry with a dimensionless spin parameter a = cJ/GM2 > 1.We calculate the relevant spin intervals for a subset of HF QPO models considered in the previous study. Our analysis indicates that for all but one of the considered models there exists at least one interval of a > 1 that is compatible with constraints given by the ranges of the central compact object mass independently estimated for the three sources. For most of the models, the inferred values of a are several times higher than the extreme Kerr black hole value a = 1. These values may be too high since the spin of superspinars is often assumed to rapidly decrease due to accretion when a >> 1. In this context, we conclude that only the epicyclic and the Keplerian resonance model provides estimates that are compatible with the expectation of just a small deviation from a = 1.

Finite escape fraction for ultrahigh energy collisions around Kerr naked singularity

We investigate the issue of observability of high-energy collisions around Kerr naked singularity and show that results are in contrast with the Kerr black hole case. We had shown that it would be possible to have ultrahigh energy collisions between the particles close to the location r = M around the Kerr naked singularity if the Kerr spin parameter transcends unity by an infinitesimally small amount a → 1+. The collision is between initially ingoing particle that turns back as an outgoing particle due to angular momentum barrier, with another ingoing particle. We assume that two massless particles are produced in such a collision and their angular distribution is isotropic in the centre-of-mass frame. We calculated the escape fraction for the massless particles to reach infinity. We showed that the escape fraction is finite and approximately equal to half for the ultrahigh energy collisions. Therefore, the particles produced in high-energy collisions would escape to infinity providing the signature of the nature of basic interactions at those energies. This result is in contrast with the case of extremal Kerr black hole where almost all particles produced in high-energy collisions are absorbed by the black hole rendering collisions unobservable.