Kerr Black Hole Research Articles

The Effects of a Minimal Length on the Kerr Metric and the Hawking Temperature

The Effects of a Minimal Length on the Kerr Metric and the Hawking Temperature

Black hole spectroscopy with ground-based atom interferometer and space-based laser interferometer gravitational wave detectors

Gravitational wave (GW) detection allows us to test general relativity in entirely new regimes. A prominent role takes the detection of quasi-normal modes (QNMs), which are emitted after the merger of a binary black hole (BBH) when the highly distorted remnant emits GWs to become a regular Kerr black hole (BH). The BH uniqueness theorems of Kerr black hole solutions in general relativity imply that the frequencies and damping times of QNMs are determined solely by the mass and spin of the remnant BH. Therefore, detecting QNMs offers a unique way to probe the nature of the remnant BH and to test general relativity. We study the detection of a merging BBH in the intermediate-mass range, where the inspiral–merger phase is detected by space-based laser interferometer detectors TianQin and LISA, while the ringdown is detected by the ground-based atom interferometer (AI) observatory AION. The analysis of the ringdown is done using the regular broadband mode of AI detectors as well as the resonant mode optimizing it to the frequencies of the QNMs predicted from the inspiral–merger phase. We find that the regular broadband mode allows constraining the parameters of the BBH with relative errors of the order 10−1 and below from the ringdown. Moreover, for a variety of systems considered, the frequencies and the damping times of the QNMs can be determined with relative errors below 0.1 and 0.2, respectively. We further find that using the resonant mode can improve the parameter estimation for the BBH from the ringdown by a factor of up to three. Utilizing the resonant mode significantly limits the detection of the frequency of the QNMs but improves the detection error of the damping times by around two orders of magnitude.

Mass and spin measurements of black hole and neutron stars X-ray binaries through axisymmetric oscillation modes of thick torus

Abstract This paper examines the oscillatory behaviour of relativistic, non-self-gravitating, charged-fluid toroidal structures within the context of the Kerr metric. The primary objective is to explore how thick accretion discs influence the mass and spin measurements of black holes and neutron stars in Low-Mass X-ray Binaries (LMXBs) through Quasi-Periodic Oscillations (QPOs) models. To achieve this, we conduct a local analysis within a general relativistic framework, determining the radial epicyclic and orbital frequencies in a perfect fluid disk. The tori are modelled using a non-Keplerian distribution of specific angular momentum, and we analyse how the oscillation properties depend on the model’s angular momentum distribution parameters. Subsequently, we connect these oscillatory frequencies to high-frequency QPOs observed in low-mass X-ray binaries, enabling us to calculate the optimal mass and spin values for each studied source.

Particle dynamics and quasi-periodic oscillations in the GUP-modified Schwarzschild spacetime: Constraint using micro-quasars data

In this work, we have worked out dynamical aspects for the particles moving around the GUP-corrected-Schwarzschild (S-GUP) black hole. We have calculated the innermost stable circular orbit (ISCO) around black hole and explored its implications for different microquasars. Additionally, we have shown that the Kerr black hole mimics S-GUP black hole after some tuning of parameters. Finally, considering the S-GUP black hole as a microquasar source, we have studied quasi-periodic oscillation (QPO). Further utilizing the available observational data of few microquasars, we have obtained constrains on the GUP parameter ϵ as well.

Loosely trapped surface for slowly rotating black hole

Abstract We construct the marginal loosely trapped surface (marginal LTS) for the Kerr spacetime with a small Kerr parameter perturbatively, where the LTS condition is saturated. An LTS is a surface that specifies the strong gravity region, which is a generalization of the photon sphere in the Schwarzschild spacetime. It turns out that there are an infinite number of marginal LTSs. At the leading order of the small Kerr parameter, all of the marginal LTSs have the same area. However, one can see that the maximal marginal LTS among them is uniquely determined at the higher order.

Self-gravitating matter in stationary and axisymmetric black hole spacetimes

Abstract All black holes (BHs) in nature are expected to be described by the Kerr vacuum solution of general relativity. However, the Kerr BH interior contains several problematic features such as a Cauchy horizon, a curvature singularity, and a causality-violating region. Non-Kerr BH models, which are used to examine the genericity of these features, typically contain nontrivial matter content. When such self-gravitating matter is minimally-coupled to Einstein–Hilbert gravity, the Einstein equations can be directly used to investigate its physical properties. We examine here the properties of matter in a broad class of stationary and axisymmetric, geodesically-integrable BH spacetimes, and how they are linked to various features of the spacetime geometry. In these spacetimes, we find the matter to typically flow along timelike Killing orbits in the BH exterior, usually exhibiting differential rotation but sometimes additionally also non-rigid rotation. At a horizon, the matter rest-frame energy density, ε, and principal normal pressure, pn , are shown to necessarily satisfy p n = − ϵ , implying that only specific types of matter can thread stationary event horizons (e.g. electromagnetic fields but not massless real scalar fields). Furthermore, we introduce Boyer–Lindquist-like coordinates for the nonstationary regions in the BH interior, which show the matter to be comoving with the interior cosmology. We also obtain simple expressions for the expansions of the ingoing and outgoing zero angular momentum null congruences and comment on the light-focussing behavior of the cosmology. Finally, we verify above results explicitly by working with a representative set of well-known BH spacetimes which contain various types of matter—scalar fields, electromagnetic fields, anisotropic fluids. Some spacetimes have singularities while others have regular interiors. In the exterior, the matter satisfies the weak energy condition. The framework developed here can be extended to cover more general spacetimes.

Spin-2 Green’s functions on Kerr in radiation gauge

Abstract We construct retarded and advanced Green’s functions for gravitational perturbations in Kerr in an ingoing radiation gauge. Our Green’s functions have a frequency domain piece that has previously been obtained by Ori (2003 Phys. Rev. D 67) based on the Chrzanowski-Cohen-Kegeles metric reconstruction method. As is well known, this piece by itself is not sufficient to obtain an actual Green’s function. We show how to complete it with a piece based on a method by Green et al (2020 Class. Quantum Grav. 37). The completion piece has a completely explicit form in the time-domain and is supported on pairs of points on the same outgoing principal null geodesic which are in the appropriate causal order. We expect our Green’s functions to be useful for gravitational self-force calculations and other perturbation problems on Kerr spacetime.

Recent Developments in Degenerate Higher Order Scalar Tensor Theories

AbstractDegenerate Higher Order Scalar Tensor (DHOST) theories are the most general scalar‐tensor theories whose Lagrangian depends on the metric tensor and a single scalar field and its derivatives up to second order. They propagate only one scalar degree of freedom, without being plagued by Ostrogradsky instabilities. This is achieved through certain degeneracies of the functions forming their Lagrangian. They generalize the Horndeski and beyond‐Horndeski theories. Originally proposed to describe the late‐time acceleration of the expansion of the universe, generalizing the cosmological constant, they can also be used to build models of the early universe, to describe inflation or alternatives to standard inflation. In the late universe, they modify the standard Vainstein screening mechanism from Horndeski theories (which can have observable consequences) and are suited to build black hole models, featuring non‐stealth Kerr black hole solutions. In this work, their phenomenology is reviewed, looking at their basic properties, their parameterizations and classifications, focusing on solutions in the early and the late universe and at cosmological and astrophysical constraints.

Inter-disks inversion surfaces

We consider a counter-rotating torus orbiting a central Kerr black hole (BH) with dimensionless spin a, and its accretion flow into the BH, in an agglomerate of an outer counter-rotating torus and an inner co-rotating torus. This work focus is the analysis of the inter-disks inversion surfaces. Inversion surfaces are spacetime surfaces, defined by the condition uϕ=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u^{\\phi }=0$$\\end{document} on the flow torodial velocity, located out of the BH ergoregion, and totally embedding the BH. They emerge as a necessary condition, related to the spacetime frame-dragging, for the counter-rotating flows into the central Kerr BH. In our analysis we study the inversion surfaces of the Kerr spacetimes for the counter-rotating flow from the outer torus, impacting on the inner co-rotating disk. Being totally or partially embedded in (internal to) the inversion surfaces, the inner co-rotating torus (or jet) could be totally or in part “shielded”, respectively, from the impact with flow with auϕ<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a u^{\\phi }<0$$\\end{document}. We prove that, in general, in the spacetimes with a<0.551\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a<0.551$$\\end{document} the co-rotating toroids are always external to the accretion flows inversion surfaces. For 0.551<a<0.886\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.551<a<0.886$$\\end{document}, co-rotating toroids could be partially internal (with the disk inner region, including the inner edge) in the flow inversion surface. For BHs with a>0.886\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a>0.886$$\\end{document}, a co-rotating torus could be entirely embedded in the inversion surface and, for larger spins, it is internal to the inversion surfaces. Tori orbiting in the BH outer ergoregion are a particular case. Further constraints on the BHs spins are discussed in the article.

Boosted Kerr–Newman black holes

Abstract In this paper we obtain a new solution of Einstein field equations which describes a boosted Kerr–Newman black hole relative to a Lorentz frame at future null infinity. To simplify our analysis we consider a particular configuration in which the boost is aligned with the black hole angular momentum. The boosted Kerr–Newman black hole is obtained considering the complete asymptotic Lorentz transformations of Robinson–Trautman coordinates to Bondi–Sachs, including the perturbation term of the boosted Robinson–Trautman metric. To verify that the final form of the metric is indeed a solution of Einstein field equations, we evaluate the corresponding energy–momentum tensor the boosted Kerr–Newman solution. To this end, we consider the electromagnetic energy–momentum tensor built with the Kerr boosted metric together with its timelike killing vector. We show that the Papapetrou field thus obtained engender an energy–momentum tensor which satisfies Einstein field equations up to 4th order for the Kerr–Newman metric. To proceed, we examine the causal structure of the boosted Kerr–Newman black hole in Bondi–Sachs coordinates as in a preferred timelike foliation. We show that the ultimate effect of a nonvanishing charge is to shrink the overall size of the event horizon and ergosphere areas when compared to the neutral boosted Kerr black holes. Considering the preferred timelike foliation we obtain the electromagnetic fields for a proper nonrotating frame of reference. We show that while the electric field displays a pure radial behavior, the magnetic counterpart develops an involved structure with two intense lobes of the magnetic field observed in the direction opposite to the boost.

Metric reconstruction in Kerr spacetime

Abstract Metric reconstruction is the general problem of parameterizing GR in terms of its two “true degrees of freedom” e.g., by a complex scalar “potential”—in practice mostly with the aim of simplifying the Einstein equation (EE) within perturbative approaches. In this paper, we re-analyze the metric reconstruction procedure by Green, Hollands, and Zimmerman (GHZ) [Class. Quant. Grav. 37, 075001 (2020)], which is a generalization of the Chrzanowski-Cohen-Kegeles (CCK) approach. Contrary to the CCK method, that by GHZ is applicable not only to the vacuum, but also to the sourced linearized Einstein equation (EE) on Kerr. Our main innovation is a version of the GHZ integration scheme that is suitable for the initial value problem of the sourced linear EE. By iteration, our scheme gives the metric to as high an order in perturbation theory as one might wish, in principle. At each order, the metric perturbation is a sum of a corrector, obtained by solving a triangular system of transport equations, a reconstructed piece, obtained from a Hertz potential as in the CCK approach, and an algebraically special perturbation, determined by the ADM quantities. As a byproduct, we determine the precise relations between the asymptotic tail of the Hertz potential in the GHZ and CCK schemes, and the quantities relevant for gravitational radiation, namely, the energy flux, news- and memory tensors, and their associated BMS-supertranslations. We also discuss ways of transforming the metric perturbation to Lorenz gauge.&amp;#xD;

Hadamard property of the Unruh state for massless fermions on Kerr spacetime: the large a case

Hadamard property of the Unruh state for massless fermions on Kerr spacetime: the large a case

Black holes, complex curves, and graph theory: Revising a conjecture by Kasner

The ratios 8/9=22/3≈0.9428 and 3/2≈0.866 appear in various contexts of black hole physics, as values of the charge-to-mass ratio Q/M or the rotation parameter a/M for Reissner-Nordström and Kerr black holes, respectively. In this work, in the Reissner-Nordström case, I relate these ratios with the quantization of the horizon area, or equivalently of the entropy. Furthermore, these ratios are related to a century-old work of Kasner, in which he conjectured that certain sequences arising from complex analysis may have a quantum interpretation. These numbers also appear in the case of Kerr black holes, but the explanation is not as straightforward. The Kasner ratio may also be relevant for understanding the random matrix and random graph approaches to black hole physics, such as fast scrambling of quantum information, via a bound related to Ramanujan graph. Intriguingly, some other pure mathematical problems in complex analysis, notably complex interpolation in the unit disk, appear to share some mathematical expressions with the black hole problem and thus also involve the Kasner ratio.

Horizon replicas in black hole shadows

Recently, new exploratory channels have opened up for the physics of highly compact objects, such as gravitational waves and black hole shadows. Moreover, more precise analysis and observations are now possible in the physics of accretion around compact objects. These advancements provide in particular an unprecedented insight into the physics near the horizons of a black hole. In this work we focus on the shadow boundary of a Kerr black hole, introducing observables related to special null orbits, called horizons replicas, solutions of the shadow edge equations which are related to particular photon orbits, defined by constraints on their impact parameter, carrying information about the angular momentum of the central spinning object. These orbits are related to particular regions on the shadow boundary and might be used to determine the spin of the black hole. The results provide the conditions by which horizon replicas are imprinted in the black hole shadow profile, in dependence on the black hole dimensionless spin and observational angle, providing eventually new templates for the future observations.

Mode analysis for the linearized Einstein equations on the Kerr metric: the large $\mathfrak{a}$ case

We give a complete analysis of mode solutions for the linearized Einstein equations and the 1 -form wave operator on the Kerr metric in the large \mathfrak{a} case. By mode solutions we mean solutions of the form e^{-it_*\sigma}\tilde{h}(r,\theta,\varphi) where t_{*} is a suitable time variable. The corresponding Fourier-transformed 1 -form wave operator and linearized Einstein operator are shown to be Fredholm between suitable function spaces and \tilde{h} has to lie in the domain of these operators. These spaces are constructed following the general framework of Vasy (2013, 2021) along the lines of Häfner et al. (2021). No mode solutions exist for \Im \sigma\ge 0,\, \sigma\neq 0 . For \sigma=0 mode solutions are Coulomb solutions for the 1 -form wave operator and linearized Kerr solutions plus pure gauge terms in the case of the linearized Einstein equations. If we fix a De Turck/wave map gauge, then the zero mode solutions for the linearized Einstein equations lie in a fixed seven-dimensional space. The proof relies on the absence of modes for the Teukolsky equation shown by Whiting (1989) and Anderson et al. (2019) and a complete classification of the gauge invariants of linearized gravity on the Kerr spacetime by Aksteiner and Bäckdahl (2018) and Aksteiner et al. (2021).

Parameter study for hot spot trajectories around SgrA*

Context. Intense flaring events in the near-infrared and X-ray wavebands of our Galactic center have been the subject of research for decades. In recent years, the GRAVITY instrument of the Very Large Telescope captured the motion and polarimetric signature of such a flare in close proximity to the supermassive black hole. Aims. This study aims to investigate a broad parameter space for hot spot motion in the vicinity of SgrA* and reproduce the observed flaring behavior. Methods. To this end, we have developed a general relativistic radiative transfer code and conducted a parameter study including both planar and ejected hot spot configurations around supermassive black holes. Results. Super-Keplerian orbital frequencies are favored by circular equatorial, cylindrical and parabolic models, whereas conical hot spot trajectories provide a better fit for orbital frequencies below the Keplerian value. Additionally, a distant observer cannot effectively differentiate between Schwarzschild and Kerr black holes, as well as face-on orbits at different observation angles.

Quasinormal Modes and Stability Analysis of Rotating Hairy Black Holes in Asymptotically Flat Spacetime

Abstract Kerr black holes, characterized solely by their mass and angular momentum, are considered the predominant type in the universe. Recent studies, however, suggest that black holes may possess additional parameters, known as “hair”. This paper investigates the quasinormal modes (QNMs) of rotating hairy black holes in asymptotically flat spacetimes using the continued fraction method to analyze their stability. Our results demonstrate that the introduction of hair parameters modifies the QNM frequencies, indicating a nuanced stability profile that reduces to the classical Kerr solution under specific conditions. These findings provide new insights into the dynamic properties of hairy black holes and their potential astrophysical implications.

Numerical investigation of the late-time tails of the solutions of the Fackerell–Ipser equation

The late-time behaviour of the solutions of the Fackerell–Ipser equation (which is a wave equation for the spin-zero component of the electromagnetic field strength tensor) on the closure of the domain of outer communication of sub-extremal Kerr spacetime is studied numerically. Within the Kerr family, the case of Schwarzschild background is also considered. Horizon-penetrating compactified hyperboloidal coordinates are used, which allow the behaviour of the solutions to be observed at the event horizon and at future null infinity as well. For the initial data, pure multipole configurations that have compact support and are either stationary or non-stationary are taken. It is found that with such initial data the solutions of the Fackerell–Ipser equation converge at late times either to a known static solution (up to a constant factor) or to zero. As the limit is approached, the solutions exhibit a quasinormal ringdown and finally a power-law decay. The exponents characterizing the power-law decay of the spherical harmonic components of the field variable are extracted from the numerical data for various values of the parameters of the initial data, and based on the results a proposal for a Price’s law relevant to the Fackerell–Ipser equation is made. Certain conserved energy and angular momentum currents are used to verify the numerical implementation of the underlying mathematical model. In the construction of these currents a discrete symmetry of the Fackerell–Ipser equation, which is the product of an equatorial reflection and a complex conjugation, is also taken into account.

Leading-order term expansion for the Teukolsky equation on subextremal Kerr black holes

Leading-order term expansion for the Teukolsky equation on subextremal Kerr black holes

Deflection of charged signals in a dipole magnetic field in Kerr background

This paper investigates charged particle deflection in a Kerr spacetime background with a dipole magnetic field, focusing on the equatorial plane and employing the weak field approximation. We employ the Jacobi–Randers metric to unify the treatment of the gravitational and electromagnetic effects on charged particles. Furthermore, we utilize the Gauss–Bonnet theorem to calculate the deflection angle through curvature integrals. The difference between the prograde and retrograde deflection angles is linked to the non-reversibility of metrics and geodesics in Finsler geometry, revealing that this difference can be considered a Finslerian effect. We analyze the impact of both gravitomagnetic field and dipole magnetic field on particle motion and deflection using the Jacobi–Randers magnetic field. The model considered in this paper exhibits interesting features in the second-order approximation of (M/b), i.e., the ratio between the spacetime mass and impact parameters. When qμ=2MaE\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q\\mu =2MaE$$\\end{document}, where q,E\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q,\\,E$$\\end{document} are the charge and asymptotic energy of the charged particle and μ,a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu ,\\,a$$\\end{document} are the dipole magnetic moment and spacetime spin, the Jacobi–Randers metric possesses reversible geodesics, leading to equal prograde and retrograde deflection angles. In this case, the gravitomagnetic field and dipole magnetic field cancel each other out, distinguishing it from scenarios involving only the gravitomagnetic field or the dipole magnetic field. We also explore the magnetic field’s impact on gravitational lensing of charged particles.