The spacetime geometry around astrophysical black holes is supposed to be well approximated by the Kerr metric, but deviations from the Kerr solution are predicted in a number of scenarios involving new physics. Broad iron K$α$ lines are commonly observed in the X-ray spectrum of black holes and originate by X-ray fluorescence of the inner accretion disk. The profile of the iron line is sensitively affected by the spacetime geometry in the strong gravity region and can be used to test the Kerr black hole hypothesis. In this paper, we extend previous work in the literature. In particular: i) as test-metric, we employ the parametrization recently proposed by Konoplya, Rezzolla, and Zhidenko, which has a number of subtle advantages with respect to the existing approaches; ii) we perform simulations with specific X-ray missions, and we consider NuSTAR as a prototype of current observational facilities and eXTP as an example of the next generation of X-ray observatories. We find a significant difference between the constraining power of NuSTAR and eXTP. With NuSTAR, it is difficult or impossible to constrain deviations from the Kerr metric. With eXTP, in most cases we can obtain quite stringent constraints (modulo we have the correct astrophysical model).
X-ray reflection spectroscopy is a powerful technique for probing the nature of gravity around black holes in the so-called strong field regime. One of the most popular of such probes is to look at theory-agnostic deviations away from the Kerr solution, which is the only astrophysically relevant black hole solution within classical general relativity, in order to verify whether astrophysical black holes are described by the Kerr metric. We have recently extended our X-ray reflection spectroscopy framework to a class of very general axisymmetric non-Kerr black holes proposed by Konoplya, Rezzol…
We propose a new parametrization for testing the Kerr nature of astrophysical black hole candidates. The common approaches focus on the attempt to constrain possible deviations from the Kerr solution described by new terms in the metric. Here we adopt a different perspective. The mass and the spin of a black hole make the spacetime curved and we want to check whether they do it with the strength predicted by general relativity. As an example, we apply our parametrization to the black hole shadow, an observation that may be possible in a not too distant future.
The construction of a generic parametrization to describe the spacetime geometry around astrophysical black hole candidates is an important step to test the Kerr black hole hypothesis. In the last few years, the Johannsen-Psaltis metric has been the most common framework to study possible deviations from the Kerr solution with present and near future observations. Recently, Cardoso, Pani and Rico have proposed a more general parametrization. The aim of the present paper is to study this new metric in a specific context, namely the thermal spectrum of geometrically thin and optically thick accr…
We discuss a parametrization to describe possible deviations from the Kerr metric and test astrophysical black hole candidates with electromagnetic radiation. Our metric is a very simple generalization of the Kerr solution with two main properties: $i)$ the phenomenology is quite rich and, for example, it can describe black holes with high Novikov-Thorne radiative efficiency or black holes of very small size; $ii)$ it is suitable for the numerical calculations required to study the spectrum of thin disks. The latter point is our principal motivation to study such a kind of parametrization, bec…
Kerr-referenced analytical parametrization of rotating black holes in dynamical Chern-Simons gravity
New Uzbekistan University（新乌兹别克斯坦大学）；Tashkent State Technical University（塔什干国立技术大学）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）；School of Physics, Harbin Institute of Technology（哈尔滨工业大学物理学院）
X-ray reflection spectroscopy is a promising technique for testing general relativity in the strong field regime, as it can be used to test the Kerr black hole hypothesis. In this context, the parametrically deformed black hole metrics proposed by Konoplya, Rezzolla \& Zhidenko (Phys. Rev. D93, 064015, 2016) form an important class of non-Kerr black holes. We implement this class of black hole metrics in \textsc{relxill\_nk}, which is a framework we have developed for testing for non-Kerr black holes using X-ray reflection spectroscopy. We perform a qualitative analysis of the effect of the le…
The present paper aims at elaborating a completely physical representation for the general 4-parameter family of the extended double-Kerr spacetimes describing two spinning sources in gravitational equilibrium. This involved problem is solved in a concise analytical form by using the individual Komar masses and angular momenta as arbitrary parameters, and the simplest equatorially symmetric specialization of the general expressions obtained by us yields the physical representation for the well-known Dietz-Hoenselaers superextreme case of two balancing identical Kerr constituents. The existence…
In a recent paper [Ghasemi-Nodehi & Bambi, EPJC 76 (2016) 290], we have proposed a new parametrization for testing the Kerr nature of astrophysical black hole candidates. In the present work, we study the possibility of constraining the "Kerr parameters" of our proposal using X-ray reflection spectroscopy, the so-called iron line method. We simulate observations with the LAD instrument on board of the future eXTP mission assuming an exposure time of 200~ks. We fit the simulated data to see if the Kerr parameters can be constrained. If we have the correct astrophysical model, 200~ks observation…
Black hole photon ring beyond General Relativity: an integrable parametrization
Arnold Sommerfeld Center for Theoretical Physics（阿诺德·索末菲理论物理中心）；Munich Center for Quantum Sciences and Technology（慕尼黑量子科学与技术中心）；Université de Lyon, ENS de Lyon, Laboratoire de Physique, CNRS UMR 5672（里昂大学，巴黎高等师范学院里昂分校，物理实验室，法国国家科学研究中心）；LUX, CNRS UMR 8262, Observatoire de Paris - PSL, Sorbonne Université Paris（卢克瑟姆天文台，法国国家科学研究中心，巴黎天文台-巴黎文理研究大学，索邦巴黎大学）；Laboratoire de Mathématiques de Bretagne Atlantique, CNRS UMR 6205, Université de Bretagne Occidental（布列塔尼大西洋数学实验室，法国国家科学研究中心，布列塔尼西部大学）
The iron K$α$ line commonly observed in the X-ray spectrum of both stellar-mass and supermassive black hole candidates originates from X-ray fluorescence of the inner accretion disk. Accordingly, it can be used to map the spacetime geometry around these objects. In this paper, we extend previous work using the iron K$α$ line to test the Kerr black hole hypothesis. We adopt the Cardoso-Pani-Rico parametrization and we test the possibility of constraining possible deviations from the Kerr solution that can be obtained from observations across the range of black hole spins and inclination angles.…
We use the continued fraction method to determine the eigenfrequencies associated with a scalar field around a Kerr-like black hole. The Kerr-like metric considered in this article is a subclass of the general parametrization of axisymmetric black holes proposed by Konoplya, Rezzolla and Zhidenko. In addition to its mass $M$ and specific angular momentum $a$, the black hole depends on a third parameter $η$, called the deformation parameter. We investigate how the deformation parameter affects the quasinormal modes and the quasibound states of a massive scalar field around the black hole. In pa…
We propose a new presentation of the Demiański-Newman (DN) solution of the axisymmetric Einstein equations. We introduce new dimensionless parameters $p$, $q$ and $s$, but keeping the Boyer-Lindquist coordinate transformation used for the Kerr metric in the Ernst method. The family of DN metrics is studied and it is shown that the main role of $s$ is to determine the singularities, which we obtain by calculating the Riemann tensor components and the invariants of curvature. So, $s$ reveals itself as the parameter of the singular rings on the inner ergosphere.
We discuss the fundamentals of classical black hole (BH) thermodynamics in a new framework determined by light surfaces and their frequencies. This new approach allows us to study BH transitions inside the Kerr geometry. In the case of BHs, we introduce a new parametrization of the metric in terms of the maximum extractable rotational energy or, correspondingly, the irreducible mass, which is an alternative to the spin parametrization. It turns out that BH spacetimes with spins $a/M= \sqrt {8/9}$ and $a/M=1/\sqrt{2}$ show anomalies in the rotational energy extraction and surface gravity wherea…
The continuum-fitting method is the analysis of the thermal spectrum of the geometrically thin and optically thick accretion disk around stellar-mass black holes. A parametrization aiming to test the Kerr nature of astrophysical black holes was proposed in Ghasemi-Nodehi and Bambi in EPJC 76: 290, 2016. The metric contains 11 parameters in addition to the mass and spin parameters. One can recover the Kerr case by setting all parameters to one. In this paper, I study the continuum-fitting method in Ghasemi-Nodehi-Bambi background. I show the impact of each of the parameters on the spectra. I th…
The reverberation associated with the iron line is the time lag between direct photons from the corona and the photons reflected from the disk. The resulting line spectrum is called the 2D transfer function. The shape of the 2D transfer function is determined by the geometry of spacetime and the properties of BH. In a paper (Ghasemi-Nodehi and Bambi in EPJC 76:290, 2016), the authors have proposed a parametrization. This parametrization is aimed to test the Kerr nature of astrophysical black hole candidates. In this paper, I provide a reverberation mapping of the Ghasemi-Nodehi-Bambi metric in…
In this paper, binary systems of unequal Kerr-Newman black holes located on the axis and apart by a massless strut are investigated. After adopting a fitting parametrization, the conditions on the axis and the one eliminating the individual magnetic charges are solved exactly with the aim to obtain a 7-parametric asymptotically flat exact solution. It is also deduced explicit analytical formulas for each half-length horizon $σ_{i}$, $i = 1,2$, in terms of arbitrary physical Komar parameters: mass $M_{i}$, electric charge $Q_{i}$, angular momentum $J_{i}$, and a coordinate distance $R$. All the…
Stationary axisymmetric binary systems of unequal counterrotating Kerr-Newman sources with a massless strut in between are studied. By means of the choice of a suitable parametrization, the axis conditions and the absence of individual magnetic charges are fulfilled; thus, the entire metric reduces to a 6-parametric asymptotically flat exact solution. Later on, with the purpose to describe interacting black holes, the analytic functional form of the horizon half-length parameter $σ_{k}$ is obtained explicitly in terms of physical Komar parameters: mass $M_{k}$, electric charge $Q_{k}$, angular…
Following previous work of ours in spherical symmetry, we here propose a new parametric framework to describe the spacetime of axisymmetric black holes in generic metric theories of gravity. In this case, the metric components are functions of both the radial and the polar angular coordinates, forcing a double expansion to obtain a generic axisymmetric metric expression. In particular, we use a continued-fraction expansion in terms of a compactified radial coordinate to express the radial dependence, while we exploit a Taylor expansion in terms of the cosine of the polar angle for the polar de…
We present a parametrization of $T^3$ and $S^1\times S^2$ Gowdy cosmological models which allows us to study both types of topologies simultaneously. We show that there exists a coordinate system in which the general solution of the linear polarized special case (with both topologies) has exactly the same functional dependence. This unified parametrization is used to investigate the existence of Cauchy horizons at the cosmological singularities, leading to a violation of the strong cosmic censorship conjecture. Our results indicate that the only acausal spacetimes are described by the Kantowsk…
SgrA$^*$, the supermassive black hole candidate at the center of our Galaxy, seems to be one of the most promising object to test the Kerr black hole hypothesis with near future observations. In a few years, it will hopefully be possible to measure a number of relativistic effects around this body, and the combination of different observations can be used to constrain possible deviations from the Kerr solution. In this paper, I discuss the combination of three promising techniques in the framework of the Cardoso-Pani-Rico parametrization: the observation of blobs of plasma orbiting near the in…
The construction of a generic parametrization of spinning geometries which can be matched continuously to the Kerr metric is an important open problem in General Relativity. Its resolution is more than of academic interest, as it allows to parametrize and quantify possible deviations from the no-hair theorem. Various approaches to the problem have been proposed, all with their own (severe) limitations. Here we discuss the metric recently proposed by Johannsen and Psaltis, showing that (i) the original metric describes only corrections that preserve the horizon area-mass relation of nonspinning…
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 …
We consider the Blandford-Znajek process of electromagnetic extraction of energy from a general axially symmetric asymptotically flat slowly rotating black hole. Using the general parametrization of the black-hole spacetime we construct formulas for the flux of the magnetic field and the rate of energy extraction, which are valid not only for the Kerr spacetime, but also for its arbitrary axially symmetric deformations. We show that in the dominant order these quantities depend only on a single deformation parameter, which relates the spin frequency of a black hole with its rotation parameter.
The mass of a Kerr black hole can be separated into irreducible and rotational components -the former is a lower limit to the energy that cannot be possibly extracted from the event horizon and is related to its area. Here we compute the irreducible masses of the stellar-mass black holes observed by gravitational-wave interferometers LIGO and Virgo. Using single-event data, we present a re-parametrization of the posterior distribution that explicitly highlights the irreducible and rotational contributions to the total energy. We exploit the area law to rank the black-hole mergers observed to d…
The Breton-Manko solution for two identical counter-rotating Kerr-Newman charged masses is rewritten in the physical parametrization involving Komar quantities. The new form of the solution turns out to be very convenient for verifying that the black-hole sector of the Bretón-Manko binary configuration saturates a recent geometric inequality for interacting black holes with struts discovered by Gabach Clement.
In this paper we present and analyze the simplest physically meaningful model for stationary black diholes - a binary configuration of counter-rotating Kerr-Newman black holes endowed with opposite electric charges - elaborated in a physical parametrization on the basis of one of the Ernst-Manko-Ruiz equatorially antisymmetric solutions of the Einstein-Maxwell equations. The model saturates the Gabach-Clement inequality for interacting black holes with struts, and in the absence of rotation it reduces to the Emparan-Teo electric dihole solution. The physical characteristics of each dihole cons…
We determine the class of axisymmetric and asymptotically flat black-hole spacetimes for which the test Klein-Gordon and Hamilton-Jacobi equations allow for the separation of variables. The known Kerr, Kerr-Newman, Kerr-Sen and some other black-hole metrics in various theories of gravity are within the class of spacetimes described here. It is shown that although the black-hole metric in the Einstein-dilaton-Gauss-Bonnet theory does not allow for the separation of variables (at least in the considered coordinates), for a number of applications it can be effectively approximated by a metric wit…
We systematically investigate axisymmetric extremal isolated horizons (EIHs) defined by vanishing surface gravity, corresponding to zero temperature. In the first part, using the Newman-Penrose and GHP formalism we derive the most general metric function for such EIHs in the Einstein-Maxwell theory, which complements the previous result of Lewandowski and Pawlowski. We prove that it depends on 5 independent parameters, namely deficit angles on the north and south poles of a spherical-like section of the horizon, its radius (area), and total electric and magnetic charges of the black hole. The …
Motivated by the lack of a general parametrization for exotic compact objects, we construct a class of perturbative solutions valid for small (but otherwise generic) multipolar deviations from a Schwarzschild metric in general relativity. We introduce two classes of exotic compact objects, with "soft" and "hard" hair, for which the curvature at the surface is respectively comparable to or much larger than that at the corresponding black-hole horizon. We extend the Hartle-Thorne formalism to relax the assumption of equatorial symmetry and to include deformations induced by multipole moments hig…
Gravitational waves from binary black holes have the potential to yield information on both of the intrinsic parameters that characterize the compact objects: their masses and spins. While the component masses are usually resolvable, the component spins have proven difficult to measure. This limitation stems in great part from our choice to inquire about the spins of the most and least massive objects in each binary, a question that becomes ill-defined when the masses are equal. In this paper we show that one can ask a different question of the data: what are the spins of the objects with the …
Constraining the geometry of rotating black holes with eikonal QNMs
Università di Napoli “Federico II”（那不勒斯费德里科二世大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Napoli（意大利国家核物理研究所，那不勒斯分部）；University of Tübingen（蒂宾根大学）
The 2017 Event Horizon Telescope (EHT) observations of the central source in M87 have led to the first measurement of the size of a black-hole shadow. This observation offers a new and clean gravitational test of the black-hole metric in the strong-field regime. We show analytically that spacetimes that deviate from the Kerr metric but satisfy weak-field tests can lead to large deviations in the predicted black-hole shadows that are inconsistent with even the current EHT measurements. We use numerical calculations of regular, parametric, non-Kerr metrics to identify the common characteristic a…
Acceleration radiation, quasinormal modes and quasi-bound states in generic rotating regular black holes
Harbin Institute of Technology（哈尔滨工业大学）；New Uzbekistan University（新乌兹别克斯坦大学）；Eastern Mediterranean University（东地中海大学）；Mapúa University（玛布亚科技学院）；National University of Uzbekistan（乌兹别克斯坦国立大学）
