Publisher’s Note: Quasinormal mode spectrum of a Kerr black hole in the eikonal limit [Phys. Rev. D<b>82</b>, 104003 (2010)]

Dolan, Sam R.

doi:10.1103/physrevd.82.109906

Cited by 29 publications

(48 citation statements)

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“…In a different approach, Dolan developed a matched-expansion formalism for Kerr black holes of arbitrary spins that can be applied to compute the frequency of QNMs, but only for modes with l ¼ jmj and m ¼ 0 [29].…”

Section: B Methods and Results Of This Articlementioning

confidence: 99%

“…For example, Zimmerman and Chen [26] (based on work by Mino and Brink [27]) study extensions to the usual spectrum of modes generated in generic ringdowns. Dolan and Ottewill use eikonal methods to approximate the modal wave function, and they use these functions to study the Green's function and to help understand wave propagation in the Schwarzschild spacetime [28][29][30].…”

Section: A Overview Of Quasinormal Modes and Their Geometric Interprmentioning

confidence: 99%

“…In Ref. [29], an alternate expression for ! I (for m ¼ 0) was computed by finding an analytic expression for the Lyapunov exponent (see Sec.…”

Section: Computing ! Imentioning

confidence: 99%

“…(52) and (53) of Ref. [29], where the next order contributions are calculated for the special cases of m ¼ l and m ¼ Àl, respectively.…”

Section: Accuracy Of the Wkb Approximationmentioning

confidence: 99%

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Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation

et al. 2012

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There is a well-known, intuitive geometric correspondence between high-frequency quasinormal modes of Schwarzschild black holes and null geodesics that reside on the light ring (often called spherical photon orbits): the real part of the mode's frequency relates to the geodesic's orbital frequency, and the imaginary part of the frequency corresponds to the Lyapunov exponent of the orbit. For slowly rotating black holes, the quasinormal mode's real frequency is a linear combination of the orbit's precessional and orbital frequencies, but the correspondence is otherwise unchanged. In this paper, we find a relationship between the quasinormal-mode frequencies of Kerr black holes of arbitrary (astrophysical) spins and general spherical photon orbits, which is analogous to the relationship for slowly rotating holes. To derive this result, we first use the Wentzel-Kramers-Brillouin approximation to compute accurate algebraic expressions for large-l quasinormal-mode frequencies. Comparing our Wentzel-Kramers-Brillouin calculation to the leading-order, geometric-optics approximation to scalar-wave propagation in the Kerr spacetime, we then draw a correspondence between the real parts of the parameters of a quasinormal mode and the conserved quantities of spherical photon orbits. At next-to-leading order in this comparison, we relate the imaginary parts of the quasinormal-mode parameters to coefficients that modify the amplitude of the scalar wave. With this correspondence, we find a geometric interpretation of two features of the quasinormal-mode spectrum of Kerr black holes: First, for Kerr holes rotating near the maximal rate, a large number of modes have nearly zero damping; we connect this characteristic to the fact that a large number of spherical photon orbits approach the horizon in this limit. Second, for black holes of any spins, the frequencies of specific sets of modes are degenerate; we find that this feature arises when the spherical photon orbits corresponding to these modes form closed (as opposed to ergodically winding) curves.

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Section: B Methods and Results Of This Articlementioning

confidence: 99%

Section: A Overview Of Quasinormal Modes and Their Geometric Interprmentioning

confidence: 99%

“…In Ref. [29], an alternate expression for ! I (for m ¼ 0) was computed by finding an analytic expression for the Lyapunov exponent (see Sec.…”

Section: Computing ! Imentioning

confidence: 99%

“…(52) and (53) of Ref. [29], where the next order contributions are calculated for the special cases of m ¼ l and m ¼ Àl, respectively.…”

Section: Accuracy Of the Wkb Approximationmentioning

confidence: 99%

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Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation

et al. 2012

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“…Due to mathematical difficulties, an exact analytic solution is not always attainable. Therefore, semi-analytical approximate and numerical methods have been proposed to calculate the quasinormal frequency (QNF) [3][4][5][6][7], for example, the Pöschl-Teller potential method [8], continued fractions method [9,10], the Horowitz-Hubeny method (HH) for anti-de Sitter spacetime [11], the WKB approximation [12][13][14], the finite difference method [15][16][17][18][19][20] and the asymptotic iteration method [21][22][23][24] among others [25][26][27].In this letter, we make use of a matrix method [28] to calculate the scalar QNF's for rotating Kerr and Kerr-Sen black hole spacetimes. By using the method of separation of variables, the radial and angular parts of the linearized perturbation equation of the scalar fields are given by [29,30] (…”

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confidence: 99%

A matrix method for quasinormal modes: Kerr and Kerr–Sen black holes

et al. 2017

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In this letter, a matrix method is employed to study the scalar quasinormal modes of Kerr as well as Kerr-Sen black holes. Discretization is applied to transfer the scalar perturbation equation into a matrix form eigenvalue problem, where the resulting radial and angular equations are derived by the method of separation of variables. The eigenvalues, quasinormal frequencies ω and angular quantum numbers λ, are then obtained by numerically solving the resultant homogeneous matrix equation. This work shows that the present approach is an accurate as well as efficient method for investigating quasinormal modes. Black holes constitute an intriguing topic in astrophysics and theoretical physics, where the gravitational force is so strong that nothing can escape from inside of its event horizon. The study of the properties of black holes might lead to insightful perspectives on quantum gravity. The observation of many astronomical phenomena, as, for instance, gravitational lensing, become more accessible when associated to very compact stellar objects such as black holes. Among others, one of the most important tools in the study of black holes is the analysis of its quasinormal mode (QNM) oscillations, which describe the late time dynamics of black holes or black hole binaries, and therefore provide valuable information on the inherent properties of the black hole spacetime as well as its stability. Recently, such signal was observed in the LIGO's first direct detection of gravitational wave [1,2]. KeywordsGenerally, the QNM problem can be reformulated in terms of a Schrödinger-type equation. Due to mathematical difficulties, an exact analytic solution is not always attainable. Therefore, semi-analytical approximate and numerical methods have been proposed to calculate the quasinormal frequency (QNF) [3][4][5][6][7], for example, the Pöschl-Teller potential method [8], continued fractions method [9,10], the Horowitz-Hubeny method (HH) for anti-de Sitter spacetime [11], the WKB approximation [12][13][14], the finite difference method [15][16][17][18][19][20] and the asymptotic iteration method [21][22][23][24] among others [25][26][27].In this letter, we make use of a matrix method [28] to calculate the scalar QNF's for rotating Kerr and Kerr-Sen black hole spacetimes. By using the method of separation of variables, the radial and angular parts of the linearized perturbation equation of the scalar fields are given by [29,30] (whereHere, a ∈ [0,] gives the angular momentum per unit mass. When b = 0, it is the Kerr-Sen black hole case, which reduces to the Kerr black hole spacetime at b = 0. For the case of Kerr black hole, in order to compare our results with those from the continuous fraction method, the mass of the black hole is taken to be M = 1/2. On the other hand, for the case of Kerr-Sen black hole, the mass M = (2b + r 0 + r i )/2 and angular momentum a = √ r i r 0 can be expressed in terms of the event horizon r 0 and the inner horizon r i . m represents the magnetic quantum number and u = cos θ ∈ [−1, 1]. It...

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Upper bound on the radii of black-hole photonspheres

Hod

2013

Physics Letters B

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One of the most remarkable predictions of the general theory of relativity is the existence of black-hole "photonspheres", compact null hypersurfaces on which massless particles can orbit the central black hole. We prove that every spherically-symmetric asymptotically flat black-hole spacetime is characterized by a photonsphere whose radius is bounded from above by $r_{\gamma} \leq 3M$, where $M$ is the total ADM mass of the black-hole spacetime. It is shown that hairy black-hole configurations conform to this upper bound. In particular, the null circular geodesic of the (bald) Schwarzschild black-hole spacetime saturates the bound.Comment: 10 page

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Publisher’s Note: Quasinormal mode spectrum of a Kerr black hole in the eikonal limit [Phys. Rev. D82, 104003 (2010)]

Cited by 29 publications

References 0 publications

Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation

Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation

A matrix method for quasinormal modes: Kerr and Kerr–Sen black holes

Upper bound on the radii of black-hole photonspheres

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