Near-extremal Kerr Black Holes Research Articles

Logarithmic Corrections to Kerr Thermodynamics

Recent work has shown that loop corrections from massless particles generate 32logTHawking corrections to black hole entropy which dominate the thermodynamics of cold near-extreme charged black holes. Here we adapt this analysis to near-extreme Kerr black holes. Like AdS2×S2, the near-horizon extreme Kerr (NHEK) metric has a family of normalizable zero modes corresponding to reparametrizations of boundary time. The path integral over these zero modes leads to an infrared divergence in the one-loop approximation to the Euclidean NHEK partition function. We regulate this divergence by retaining the leading finite temperature correction in the NHEK scaling limit. This “not-NHEK” geometry lifts the eigenvalues of the zero modes, rendering the path integral infrared finite. The quantum-corrected near-extremal entropy exhibits 32logTHawking behavior characteristic of the Schwarzian model and predicts a lifting of the ground state degeneracy for the extremal Kerr black hole. Published by the American Physical Society 2024

The correspondence between rotating black holes and fundamental strings

The correspondence principle between strings and black holes is a general framework for matching black holes and massive states of fundamental strings at a point where their physical properties (such as mass, entropy and temperature) smoothly agree with each other. This correspondence becomes puzzling when attempting to include rotation: At large enough spins, there exist degenerate string states that seemingly cannot be matched to any black hole. Conversely, there exist black holes with arbitrarily large spins that cannot correspond to any single-string state. We discuss in detail the properties of both types of objects and find that a correspondence that resolves the puzzles is possible by adding dynamical features and non-stationary configurations to the picture. Our scheme incorporates all black hole and string phases as part of the correspondence, save for one outlier which remains enigmatic: the near-extremal Kerr black hole. Along the way, we elaborate on general aspects of the correspondence that have not been emphasized before.

Photon rings around warped black holes

The black hole photon ring is a prime target for upcoming space-based VLBI missions seeking to image the fine structure of astrophysical black holes. The classical Lyapunov exponents of the corresponding nearly bound null geodesics control the quasinormal ringing of a perturbed black hole as it settles back down to equilibrium, and they admit a holographic interpretation in terms of quantum Ruelle resonances of the microstate dual to the Kerr black hole. Recent work has identified a number of emergent symmetries related to the intricate self-similar structure of the photon ring. Here, we explore this web of interrelated phenomena in an exactly soluble example that arises as an approximation to the near-extremal Kerr black hole. The self-dual warped AdS3 geometry has a photon ring as well as isometries and an exactly calculable quasinormal mode (QNM) spectrum. We show explicitly that the geometric optics approximation reproduces the eikonal limit of the exact scalar QNM spectrum, as well as the approximate ‘near-ring’ wavefunctions. The isometries are directly related to the emergent conformal symmetry of the photon ring in black hole images but are distinct from a recently discussed conformal symmetry of the eikonal QNM spectrum. The equivalence of the classical QNM spectrum—and thus the photon ring—to the quantum Ruelle resonances in the context of a spacetime with a putative holographic dual suggests that the photon ring of a warped black hole is indeed part of the black hole hologram.

Quasinormal resonances of rapidly-spinning Kerr black holes and the universal relaxation bound

The universal relaxation bound suggests that the relaxation times of perturbed thermodynamical systems is bounded from below by the simple time-times-temperature (TTT) quantum relation τ×T≥ħπ. It is known that some perturbation modes of near-extremal Kerr black holes in the regime MTBH/ħ≪m−2 are characterized by normalized relaxation times πτ×TBH/ħ which, in the approach to the limit MTBH/ħ→0, make infinitely many oscillations with a tiny constant amplitude around 1 and therefore cannot be used directly to verify the validity of the TTT bound in the entire parameter space of the black-hole spacetime (Here {TBH,M} are respectively the Bekenstein-Hawking temperature and the mass of the black hole, and m is the azimuthal harmonic index of the linearized perturbation mode). In the present compact paper we explicitly prove that all rapidly-spinning Kerr black holes respect the TTT relaxation bound. In particular, using analytical techniques, it is proved that all black-hole perturbation modes in the complementary regime m−1≪MTBH/ħ≪1 are characterized by relaxation times with the simple dimensionless property πτ×TBH/ħ≥1.

Numerical computation of second-order vacuum perturbations of Kerr black holes

Motivated by the desire to understand the leading-order nonlinear gravitational wave interactions around arbitrarily rapidly rotating Kerr black holes, we describe a numerical code designed to compute second-order vacuum perturbations on such spacetimes. A general discussion of the formalism we use is presented in [N. Loutrel et al., Phys. Rev. D 103, 104017 (2021)]; here we show how we numerically implement that formalism with a particular choice of coordinates and tetrad conditions and give example results for black holes with dimensionless spin parameters $a=0.7$ and $a=0.998$. We first solve the Teukolsky equation for the linearly perturbed Weyl scalar ${\mathrm{\ensuremath{\Psi}}}_{4}^{(1)}$, followed by direct reconstruction of the spacetime metric from ${\mathrm{\ensuremath{\Psi}}}_{4}^{(1)}$, and then solve for the dynamics of the second-order perturbed Weyl scalar ${\mathrm{\ensuremath{\Psi}}}_{4}^{(2)}$. This code is a first step toward a more general purpose second-order code, and we outline how our basic approach could be further developed to address current questions of interest, including extending the analysis of ringdown in black hole mergers to before the linear regime, exploring gravitational wave ``turbulence'' around near-extremal Kerr black holes, and studying the physics of extreme mass ratio inspiral.

Relativistic reflection spectra of super-spinning black holes

We construct a relativistic reflection model in a non-Kerr spacetime in which, depending on the value of the deformation parameter of the metric, there are black hole solutions with spin parameter |a_*| > 1. We apply our model to fit Suzaku data of four Seyfert galaxies (Ton S180, Ark 120, 1H0419–577, and Swift J0501.9–3239). These galaxies host at the center supermassive black holes that were previously interpreted as near-extremal Kerr black holes. For Ton S180 and 1H0419–577, our measurements are still consistent with the Kerr hypothesis. For Ark 120 and Swift J0501.9–3239, the Kerr solution is not recovered at 3-sigma . We discuss our results and possible systematic uncertainties in the model.

Near-horizon geodesics of high spin black holes

We provide an exhaustive and illustrated classification of timelike and null geodesics in the near-horizon region of near-extremal Kerr black holes. The classification of polar motion extends to Kerr black holes of arbitrary spin. The classification of radial motion leads to a simple parametrization of the separatrix between bound and unbound motion. Furthermore, we prove that each timelike or null geodesic is related via conformal transformations and discrete symmetries to spherical orbits and we provide the explicit mappings. We detail the high-spin behavior of both the innermost stable and the innermost bound spherical orbits.

Observability of the innermost stable circular orbit in a near-extremal Kerr black hole

We consider the escape probability of a photon emitted from the innermost stable circular orbit (ISCO) of a rapidly rotating black hole. As an isotropically emitting light source on a circular orbit reduces its orbital radius, the escape probability of a photon emitted from it decreases monotonically. The escape probability evaluated at the ISCO also decreases monotonically as the black hole spin increases. When the dimensionless Kerr parameter $a$ is at the Thorne limit $a=0.998$, the escape probability from the ISCO is $58.8\%$. In the extremal case $a=1$, even if the orbital radius of the light source is arbitrarily close to the ISCO radius, which coincides with the horizon radius, the escape probability remains at $54.6\%$. We also show that such photons that have escaped from the vicinity of the horizon reach infinity with sufficient energy to be potentially observed because Doppler blueshift due to relativistic beaming can overcome the gravitational redshift. Our findings indicate that signs of the near-horizon physics of a rapidly rotating black hole will be detectable on the edge of its shadow.

Jackiw-Teitelboim gravity and rotating black holes

We show that the free energy at low temperatures for near-extremal black holes is correctly obtained from the Jackiw-Teitelboim (JT) model of gravity. Our arguments apply to all black holes, including rotating ones, whose metric has a near-horizon AdS2 factor and the associated SL (2, ℝ) symmetry. We verify these arguments by explicit calculations for rotating black holes in 4 and 5 dimensions. Our results suggest that the JT model could prove useful in analysing the dynamics of near-extremal Kerr black holes found in nature.

Observability of spherical photon orbits in near-extremal Kerr black holes

We investigate the spherical photon orbits in near-extremal Kerr spacetimes. We show that the spherical photon orbits with impact parameters in a finite range converge on the event horizon. Furthermore, we demonstrate that the Weyl curvature near the horizon does not generate the shear of a congruence of such light rays. Because of this property, a series of images produced by the light orbiting around a near-extremal Kerr black hole several times can be observable.

Spectroscopy of extremal and near-extremal Kerr black holes

We investigate linear, spin-field perturbations of Kerr black holes in the extremal limit throughout the complex-frequency domain. We calculate quasi-normal modes of extremal Kerr, as well as of near-extremal Kerr, via a novel approach: using the method of Mano, Suzuki and Takasugi (MST). We also show how, in the extremal limit, a branch cut is formed at the superradiant-bound frequency, $\omega_{SR}$, via a simultaneous accumulation of quasi-normal modes and totally-reflected modes. For real frequencies, we calculate the superradiant amplification factor, which yields the amount of rotational energy that can be extracted from a black hole. In the extremal limit, this factor is the largest and it displays a discontinuity at $\omega_{SR}$ for some modes. Finally, we find no exponentially-growing modes nor branch points on the upper-frequency plane in extremal Kerr after a numerical investigation, thus providing evidence of the mode-stability of this space-time away from the horizon.

The gravitational two-body system: The role of the Thorne hoop conjecture

The innermost stable circular orbit (ISCO) of a black-hole spacetime marks the boundary between stable circular geodesics of test particles and unstable geodesics that plunge into the central compact object. In the present compact paper we use the famous Thorne hoop conjecture in order to address the following physically intriguing question: Does the gravitating two-body system possess an ISCO for arbitrarily large values of the dimensionless particle-to-black-hole mass ratio $\bar{\mu}\equiv \mu/M$ ? Interestingly, analyzing the role of the hoop conjecture in this gravitating two-body system, we provide compelling evidence that the answer to this seemingly simple question may be negative in the regime $ \delta\equiv (M-a)/M\ll 1$ of near-extremal Kerr black holes. In particular, it is pointed out that, according to the Thorne hoop conjecture, a co-rotating particle that moves along the ISCO of a rapidly spinning Kerr black hole may be engulfed by a larger horizon (with $ r_{\rm horizon} > r_{\rm ISCO}$ ) if its dimensionless mass parameter lies in the regime $ \bar{\mu}\gtrsim \delta^{2/3}$ . To the best of our knowledge, this important conclusion, which is a direct consequence of the Thorne hoop conjecture, has gone unnoticed in the physics literature for almost five decades.

Observational signatures of near-extremal Kerr-like black holes in a modified gravity theory at the Event Horizon Telescope

We study the shadows cast by near-extremal Kerr-MOG black holes for different values of the parameter in modified gravity (MOG). In particular, we consider an isotropic emitter orbiting near such black holes and analytically compute the positions, fluxes and redshift factors of their images. The size of the shadow decreases when the modified parameter is increased. For each shadow, the images of the emitter appear on a special part of the shadow which has a rich structure. The primary image and secondary images are similar to those produced for the near-extremal (high spin) Kerr black hole, but the near-extremal Kerr-MOG black hole can have a spin ($\hat{J}/M^2_{\alpha}$) which is finitely lower than 1. When the modified parameter is varied, the typical positions of the corresponding images do not change, nor does the typical redshift factor associated with the primary image. However, another typical redshift factor associated with the secondary image increases when the modified parameter is increased. We also find that the fluxes increase in that case. These images appear periodically with period greater than that of Kerr. This provides an alternative signature away from the Kerr case which may be tested by the Event Horizon Telescope.

Analytical study of a Kerr-Sen black hole and a charged massive scalar field

It is reported that Kerr-Newman and Kerr-Sen black holes are unstable to perturbations of charged massive scalar field. In this paper, we study analytically the complex frequencies which characterize charged massive scalar fields in a near-extremal Kerr-Sen black hole. For near-extremal Kerr-Sen black holes and for charged massive scalar fields in the eikonal large-mass $\mathcal{M}\ensuremath{\gg}\ensuremath{\mu}$ regime, where $\mathcal{M}$ is the mass of the black hole, and $\ensuremath{\mu}$ is the mass of the charged scalar field, we have obtained a simple expression for the dimensionless ratio ${\ensuremath{\omega}}_{I}/({\ensuremath{\omega}}_{R}\ensuremath{-}{\ensuremath{\omega}}_{c})$, where ${\ensuremath{\omega}}_{I}$ and ${\ensuremath{\omega}}_{R}$ are, respectively, the imaginary and real parts of the frequency of the modes, and ${\ensuremath{\omega}}_{c}$ is the critical frequency for the onset of super-radiance. We have also found our expression is consistent with the result of Hod [Phys. Rev. D 94, 044036 (2016)] for the case of a near-extremal Kerr-Newman black hole and the result of Zouros and Eardly [Ann. Phys. (N.Y.) 118, 139 (1979)] for the case of neutral scalar fields in the background of a near-extremal Kerr black hole.

Destroying a Kerr Black Hole

Based on three fundamentals aspects presented by Penrose, Wald, and Hawking, the black hole’s destroying scenario can be made. The main problem of this destroying process is about the presence of black hole’s angular momentum and charge. Especially for this research which is only taking an action into a rotating uncharged black hole (Kerr Black Hole). This research showed that in order to destroy a Kerr Black Hole (especially a near-extremal Kerr Black Hole) , one needs to remove its angular momentum instead by forcing it in extremal conditions and let Hawking Radiation occurs. On the other hand, the research showed that particle’s mass is linearly dependant in Penrose Process. The result also showed (which ; is a black hole’s angular momentum and is a black hole mass) cannot be reached because only black hole with negative net-energy can fulfil the condition. In another side, we calculated the minimum power needed by hole to kick the particles out. DOI: http://dx.doi.org/10.17977/um024v2i12017p007

Transient instability of rapidly rotating black holes

We analytically study the linear response of a near-extremal Kerr black hole to external scalar, electromagnetic, and gravitational field perturbations. We show that the energy density, electromagnetic field strength, and tidal force experienced by infalling observers exhibit transient growth near the horizon. The growth lasts arbitrarily long in the extremal limit, reproducing the horizon instability of extremal Kerr. We explain these results in terms of near-horizon geometry and discuss potential astrophysical implications.

On the branching of the quasinormal resonances of near-extremal Kerr black holes

It has recently been shown by Yang et al. (Phys Rev D 87:041502(R), 2013a; Phys Rev D 88:044047, 2013b) that rotating Kerr black holes are characterized by two distinct sets of quasinormal resonances. These two families of quasinormal resonances display qualitatively different asymptotic behaviors in the extremal (\(a/M\rightarrow 1\)) black-hole limit: the zero-damping modes are characterized by relaxation times which tend to infinity in the extremal black-hole limit (\(\mathfrak {I}\omega \rightarrow 0\) as \(a/M\rightarrow 1\)), whereas the damped modes (DMs) are characterized by non-zero damping rates (\(\mathfrak {I}\omega \rightarrow \) finite-values as \(a/M\rightarrow 1\)). In this paper we refute the claim made by Yang et al. that co-rotating DMs of near-extremal black holes are restricted to the limited range \(0\le \mu \lesssim \mu _{\text {c}}\approx 0.74\), where \(\mu \equiv m/l\) is the dimensionless ratio between the azimuthal harmonic index m and the spheroidal harmonic index l of the perturbation mode. In particular, we use an analytical formula originally derived by Detweiler in order to prove the existence of DMs (damped quasinormal resonances which are characterized by finite\(\mathfrak {I}\omega \) values in the \(a/M\rightarrow 1\) limit) of near-extremal black holes in the \(\mu >\mu _{\text {c}}\) regime, the regime which was claimed by Yang et al. not to contain DMs. We show that these co-rotating DMs (in the regime \(\mu >\mu _{\text {c}}\)) are expected to characterize the resonance spectra of rapidly rotating (near-extremal) black holes with \(a/M\gtrsim 1-10^{-9}\).

Self-force as a cosmic censor in the Kerr overspinning problem

It is known that a near-extremal Kerr black hole can be spun up beyond its extremal limit by capturing a test particle. Here we show that overspinning is always averted once backreaction from the particle’s own gravity is properly taken into account. We focus on nonspinning, uncharged, massive particles thrown in along the equatorial plane and work in the first-order self-force approximation (i.e., we include all relevant corrections to the particle’s acceleration through linear order in the ratio, assumed small, between the particle’s energy and the black hole’s mass). Our calculation is a numerical implementation of a recent analysis by two of us [Phys. Rev. D 91, 104024 (2015)], in which a necessary and sufficient “censorship” condition was formulated for the capture scenario, involving certain self-force quantities calculated on the one-parameter family of unstable circular geodesics in the extremal limit. The self-force information accounts both for radiative losses and for the finite-mass correction to the critical value of the impact parameter. Here we obtain the required self-force data and present strong evidence to suggest that captured particles never drive the black hole beyond its extremal limit. We show, however, that, within our first-order self-force approximation, it is possible to reach the extremal limit with a suitable choice of initial orbital parameters. To rule out such a possibility would require (currently unavailable) information about higher-order self-force corrections.

Force-free magnetosphere on near-horizon geometry of near-extreme Kerr black holes

We study force-free magnetospheres in the Blandford-Znajek process from rapidly rotating black holes by adopting the near-horizon geometry of near-extreme Kerr black holes (near-NHEK). It is shown that the Znajek regularity condition on the horizon can be directly derived from the resulting stream equation. In terms of the condition, we split the full stream equation into two separate equations. Approximate solutions around the rotation axis are derived. They are found to be consistent with previous solutions obtained in the asymptotic region. The solutions indicate energy and angular-momentum extraction from the hole.

Fast plunges into Kerr black holes

Most extreme-mass-ratio-inspirals of small compact objects into supermassive black holes end with a fast plunge from an eccentric last stable orbit. For rapidly rotating black holes such fast plunges may be studied in the context of the Kerr/CFT correspondence because they occur in the near-horizon region where dynamics are governed by the infinite dimensional conformal symmetry. In this paper we use conformal transformations to analytically solve for the radiation emitted from fast plunges into near-extreme Kerr black holes. We find perfect agreement between the gravity and CFT computations.