Dehnen $(1,4,\frac32)$ dark matter halo has been proven to be a valuable model for describing the surface brightness distributions of elliptical galaxies, yet its implications for black hole spacetimes remain largely unexplored. In this work, we construct a novel exact black hole solution embedded in this Dehnen halo and investigate its physical consequences. The influence of the halo on black hole thermodynamics is analyzed through the mass function, entropy, Hawking temperature, heat capacity, and Gibbs free energy, allowing us to assess both local and global thermodynamic stability of the black hole-dark matter system. Our results show that the presence of a Dehnen-type halo not only stabilizes the otherwise thermodynamically unstable Schwarzschild black hole but also induces phase transitions. In addition, we study null geodesics to examine photon motion, the shadow radius and the optical appearance of the system. The dark matter halo modifies the effective potential, leading to observable changes in the photon sphere and the apparent size of the shadow. We also explore the instability of circular null geodesics and its relation to quasinormal modes in an eikonal limit. These findings highlight the significant role of realistic dark matter distributions in shaping both the thermodynamic behavior and the observable signatures of black holes, providing further insight into the interplay between dark matter halos and central black holes in galaxies.
Black hole `spectroscopy', i.e. the identification of quasinormal mode frequencies via gravitational wave observations, is a powerful technique for testing the general relativistic nature of black holes. In theories of gravity beyond general relativity perturbed black holes are typically described by a set of coupled wave equations for the tensorial field and the extra scalar/vector degrees of freedom, thus leading to a theory-specific quasinormal mode spectrum. In this paper we use the eikonal/geometric optics approximation to obtain analytic formulae for the frequency and damping rate of the…
Shadow, ISCO, Quasinormal modes, Hawking spectrum, Weak Gravitational lensing, and parameter estimation of a Schwarzschild Black Hole Surrounded by a Dehnen Type Dark Matter Halo
In a recent series of papers we have shown how the eikonal/geometrical optics approximation can be used to calculate analytically the fundamental quasinormal mode frequencies associated with coupled systems of wave equations, which arise, for instance, in the study of perturbations of black holes in gravity theories beyond General Relativity. As a continuation to this series, we here focus on the quasinormal modes of nonrotating black holes in scalar Gauss-Bonnet gravity assuming a small-coupling expansion. We show that the axial perturbations are purely tensorial and are described by a modifi…
In this work, we study the relation of the eikonal quasinormal modes (EQNMs) and the unstable fundamental photon orbits (UFPOs) in the Kerr-Newman spacetime. We find that in the eikonal limit the gravitational and electromagnetic perturbations of the Kerr-Newman black hole are naturally decoupled, and a single one-dimensional Schrödinger-like equation encoding the QNM spectrum can be derived. We then show that the decoupled Teukolsky master equation and the Klein-Gordon equation for the massless scalar field in the Kerr-Newman spacetime are of the same form in the eikonal limit. As a direct co…
Quasinormal modes in the high frequency (eikonal) regime can be obtained analytically as the Mashhoon-Will-Schiutz WKB formula is exact in this case. This regime is interesting because of the correspondence between eikonal quasinormal modes and null geodesics, as well as due to existence of potential eikonal instabilities in some theories of gravity. At the same time in a number of studies devoted to quasinormal modes of spherically symmetric black holes this opportunity was omitted. Here we find analytical quasinormal modes of black holes in various alternative and extended theories of gravit…
It is well established that the response of a black hole to a generic perturbation is characterized by a spectrum of damped resonances, called quasinormal modes; and that, in the limit of large angular momentum ($l \gg 1$), the quasinormal mode frequency spectrum is related to the properties of unstable null orbits. In this paper we develop an expansion method to explore the link. We obtain new closed-form approximations for the lightly-damped part of the spectrum in the large-$l$ regime. We confirm that, at leading order in $l$, the resonance frequency is linked to the orbital frequency, and …
Gravitational Spectra and Wave Propagation in Regular Black Holes Supported by a Dehnen Halo
University of Hradec Králové（赫拉德茨克拉洛韦大学）；National Research University TIIAME（塔什干国立研究大学TIIAME）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）；Mamun University（马蒙大学）；Urgench State University（urgench国立大学）
A First-Order Eikonal Framework for Quasinormal Modes, Shadows, Strong Lensing, and Grey-Body Factors in a Scalarized Black-Hole Metric
University of Hradec Králové（赫拉德茨克拉洛韦大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）；New Uzbekistan University（新乌兹别克斯坦大学）；Tashkent International University of Education（塔什干国际教育大学）；Kimyo International University in Tashkent（塔什干基莫国际大学）；Mamun University（马蒙大学）
We compute the quasinormal frequencies of $d$-dimensional spherically symmetric black holes with leading string $α'$ corrections in the eikonal limit for tensorial gravitational perturbations and scalar test fields. We find that, differently than in Einstein gravity, the real parts of the frequency are no longer equal for these two cases. The corresponding imaginary parts remain equal to the principal Lyapunov exponent corresponding to circular null geodesics, to first order in $α'$. We also compute the radius of the shadow cast by these black holes.
The quasinormal modes (QNMs) of a regular black hole with charge are calculated in the eikonal approximation. In the eikonal limit the QNMs of black hole are determined by the parameters of the unstable circular null geodesics. The behaviors of QNMs are compared with QNMs of Reisner-Nordström black hole, it is done by fixing some of the parameters that characterize the black holes and varying another. We observed that the parameter that is related one effective cosmological constant at small distances , determines the behaviors of the QNMs of regular black hole with charge.
In Phys. Rev. D 79, 064016 (2009) it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein-Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Co…
Much of our physical intuition about black hole quasinormal modes in general relativity comes from the eikonal/geometric optics approximation. According to the well-established eikonal model, the fundamental quasinormal mode represents wavepackets orbiting in the vicinity of the black hole's geodesic photon ring, slowly peeling off towards the event horizon and infinity. Besides its strength as a "visualisation" tool, the eikonal approximation also provides a simple quantitative method for calculating the mode frequency, in close agreement with rigorous numerical results. In this paper we move…
The expressions for the quasinormal modes (QNMs) of black holes with nonlinear electrodynamics, calculated in the eikonal approximation, are presented. In the eikonal limit QNMs of black holes are determined by the parameters of the circular null geodesics. The unstable circular null orbits are derived from the effective metric that is the one obeyed by light rays under the influence of a nonlinear electromagnetic field. As an illustration we calculate the QNMs of four nonlinear electromagnetic black holes, two singular and two regular, namely from Euler-Heisenberg and Born-Infeld theories, fo…
In this paper, we study the shadow of a 4D Einstein-Gauss-Bonnet black hole as photons couple to the Weyl tensor and find that the propagation of light depends on its polarization which leads to the existence of a double shadow. Then, we discuss the effect of the coupling parameter $λ$, the polarization of light and the Gauss-Bonnet coupling constant $α$ on shadow. Further we explore the influence of the Gauss-Bonnet coupling constant $α$ on the quasinormal modes (QNMs) of massless scalar field and investigate the connection between the real part of QNMs in the eikonal limit and the shadow rad…
The geometric optics approximation provides an interpretation for eikonal correspondence that, in black-hole-containing spacetimes, connects high-frequency black hole quasinormal modes with closed photon orbits around said black hole. This correspondence has been identified explicitly for Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman black holes, the violation of which can be a potential hint toward physics beyond General Relativity. Notably, the aforementioned black hole spacetimes have sufficient symmetries such that both the geodesic equations and the master wave equations are se…
In the scope of black hole spectroscopy, several attempts have been made in the past decades in order to test black holes or gravitational theories via black hole quasinormal modes. In the eikonal approximation, the quasinormal modes are generically associated with the photon ring of the black hole. This correspondence is valid for most cases in general relativity, but may not be true in other theories of gravity. In this paper, we consider the generalized energy-momentum squared gravity in which matter fields are non-minimally coupled to geometry. We investigate the axial perturbations of the…
Rotating black holes surrounded by PFDM in STVG: Shadows and eikonal quasinormal modes
Shanghai University（上海大学）；Fuzhou University（福州大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）；Kimyo International University in Tashkent（塔什干基莫国际大学）；Tashkent State Technical University（塔什干国立技术大学）
In this contribution we study the birefringence and the quasinormal modes (QNM) in the eikonal approximation, of the Einstein-Euler-Heisenberg black hole (EEH-BH) . The EEH-BH is an exact solution of the Einstein equations coupled to the Euler-Heisenberg nonlinear electrodynamics. It is well known that in the presence of strong electromagnetic fields light rays modify their trajectories and do follow the null geodesics of an effective metric as a result of the nonlinear interaction between light and the intense magnetic or electric background. In the Euler-Heisenberg theory the phenomenon of b…
In this paper, we have studied QNM modes and absorption cross sections of Born-Infeld-de Sitter black holes. WKB approximation is employed to compute the QNM modes of massless scalar fields. We have also used null geodesics to compute quasi-normal modes in the eikonal approximation. In the eikonal limit QNMs of black holes are determined by the parameters of the circular null geodesics. Unstable circular null orbits are derived from the effective metric which is obeyed by light rays under the influence of a nonlinear electromagnetic field. Comparison is shown with the QNM of the linear electro…
In this paper, we investigate the shadow radius and quasinormal modes of a four-dimensional magnetically charged Einstein-Gauss-Bonnet Bardeen black hole and point out a simple connection between them in the eikonal limit. By studying a massless scalar field perturbation in this spacetime background and using the sixth-order Wentzel-Kramers-Brillouin(WKB) approximation, we get the quasinormal modes(QNMs) and perform a detailed analysis. It shows that the quasinormal modes are depend on the Gauss-Bonnet coupling constant and the magnetic charge. We also give a formula of the QNMs and shadow rad…
It has long been known that null unstable geodesics are related to the characteristic modes of black holes-- the so called quasinormal resonances. The basic idea is to interpret the free oscillations of a black hole in the eikonal limit in terms of null particles trapped at the unstable circular orbit and slowly leaking out. The real part of the complex quasinormal resonances is related to the angular velocity at the unstable null geodesic. The imaginary part of the resonances is related to the instability timescale (or the inverse Lyapunov exponent) of the orbit. While this geometric-optics d…
Geodesic structure, eikonal quasinormal modes and thermodynamic properties of a Schwarzschild-de Sitter-like black hole with global monopole in Bumblebee gravity
The purpose of this paper is to study quasinormal modes (QNM) of the Bardeen black hole due to scalar perturbations. We have done a thorough analysis of the QNM frequencies by varying the charge $q$, mass $M$ and the spherical harmonic index $l$. The unstable null geodesics are used to compute the QNM's in the eikonal limit. Furthermore, massive scalar field modes are also studied by varying the mass of the field. Comparisons are done with the QNM frequencies of the Reissner-Nordstrom black hole.
We study characteristic (quasinormal) modes of a $D$-dimensional Schwarzshild black hole. It proves out that the real parts of the complex quasinormal modes, representing the real oscillation frequencies, are proportional to the product of the number of dimensions and inverse horizon radius $\sim D r_{0}^{-1}$. The asymptotic formula for large multipole number $l$ and arbitrary $D$ is derived. In addition the WKB formula for computing QN modes, developed to the 3rd order beyond the eikonal approximation, is extended to the 6th order here. This gives us an accurate and economic way to compute q…
The possibility of testing gravity theories with the help of gravitational wave detections has become an interesting arena of recent research. In this paper, we follow this direction by investigating the quasinormal modes (QNMs) of the axial perturbations for charged black holes in the Palatini-type theories of gravity, specifically ($i$) the Palatini $f(R)$ gravity coupled with Born-Infeld nonlinear electrodynamics and ($ii$) the Eddington-inspired-Born-Infeld gravity (EiBI) coupled with Maxwell electromagnetic fields. The coupled master equations describing perturbations of charged black hol…
In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a charged black hole in presence of quintessence. The result shows that the shadow radius decreases with the increase of the electric charge. The quasinormal modes are derived by the sixth WKB approximation method and shadow radius, respectively. For the fixed electric charge and multipole number, the values of the real and imaginary parts of the quasinormal modes decrease with the increase of the quintessence charge. When the value of the multipole number is large, the quasinormal modes derived by the two …
In this paper, the quasinormal modes of gravitational perturbation around some well-known regular black holes were evaluated by using the WKB approximation as well as the asymptotic iteration method. Through numerical calculation, we make a detailed analysis of the gravitational QNM frequencies by varying the characteristic parameters of the gravitational perturbation and the spacetime charge parameters of the regular black holes. It is found that the imaginary part of quasinormal modes as a function of the charge parameter has different monotonic behaviors for different black hole spacetimes.…
We find the low lying quasinormal mode frequencies of the recently proposed novel four dimensional Gauss-Bonnet de Sitter black holes for scalar, electromagnetic and Dirac field perturbations using the third order WKB approximation as well as Padé approximation, as an improvement over WKB. We figure out the effect of the Gauss-Bonnet coupling $α$ and the cosmological constant $Λ$ on the real and imaginary parts of the QNM frequencies. We also study the greybody factors and eikonal limits in the above background for all three different types of perturbations.
In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a $4$-dimensional black hole with a deficit solid angle and quintessence-like matter. We find that the radii of the photon sphere and shadow decrease with the decreases of the deficit solid angle and density of quintessence-like matter. The quasinormal modes are gotten by the sixth order WKB approximation method and shadow radius, respectively. The values of the real part and imaginary parts of the quasinormal modes increase with the decrease of the values of the deficit solid angle and density of quintesse…
Eikonal Ringing, Shadows, Lensing, Grey-Body Factors, and Binding Energy of Asymptotically Flat Regular Black Holes in Phantom Dirac-Born-Infeld Gravity
Institute of Fundamental and Applied Research, National Research University TIIAME（国立研究大学塔什干信息技术与工程研究所基础与应用研究院）；Theoretical Physics Department, Samarkand State University（撒马尔罕国立大学理论物理系）；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）
The correspondence between the shadow radius and the quasi-normal modes of the Kerr-Sen black hole is studied. By using the equation of the shadow radius of the Kerr-Sen black hole and the angular separation constant of the quasi-normal modes, the expression of the real part of quasi-normal modes related to the shadow radius is obtained. We found that in the eikonal limit, our formula coincides with the previous result. Moreover, we also calculate the energy emission rate of the Kerr-Sen black hole, it turns out that the peak energy emissivity is inversely correlated with the charge parameter.
