A connection between the asymptotic iteration method and the continued fractions formalism

Matamala, Adelio R.; Gutierrez, F.A.; Diaz-Valdes, J. F.

doi:10.1016/j.physleta.2006.09.015

Cited by 8 publications

(15 citation statements)

References 15 publications

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“…As was noted in Ref. [8], the AIM and CFM are closely connected. However, the correspondence espoused by Ref.…”

Section: The Asymptotic Iteration Methodssupporting

confidence: 56%

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Quasi-normal modes of spin-3/2 fields in $D$-dimensional Reissner-Nordström black hole spacetimes using the continued fraction method

Cornell¹,

Harmsen²

2018

Preprint

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In a recent paper we calculated the field equations of spin-3/2 fields in a Ddimensional Reissner-Nordström black hole spacetime whilst maintaining the gauge symmetry of the Rarita-Schwinger equation. We were also able to determine the quasi-normal modes of the associated gauge invariant variables using the WKB approximation and the asymptotic iteration method (AIM). However, it was found that for higher dimension, and especially for the near extremal cases, the effective potential developed another maximum. The shape of the potential posed difficulties for the WKB approximations, as well as the AIM. As such, in this proceedings we would like to explore the connection between the AIM and the continued fraction method, and determine a possible reason for the difficulty in calculating the quasi-normal modes for spin-3/2 fields in this spacetime.

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“…As was noted in Ref. [8], the AIM and CFM are closely connected. However, the correspondence espoused by Ref.…”

Section: The Asymptotic Iteration Methodssupporting

confidence: 56%

“…As such, it is the aim of this proceedings to investigate these unreliable quasi-normal frequencies with a third method for calculating QNMs, that of the continued fraction method (CFM) [7], and to test the claim that the AIM and the CFM are connected [8].…”

Section: Introductionmentioning

confidence: 99%

Quasi-normal modes of spin-3/2 fields in $D$-dimensional Reissner-Nordström black hole spacetimes using the continued fraction method

Cornell¹,

Harmsen²

2018

Preprint

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“…The study of quasinormal modes (QNMs) of the Schwarzschild black hole is an old and well established subject (for a recent review see reference [1] and references therein), where the various frequencies have been well determined, typically by applying a Frobenius series solution approach, leading to continued fractions for QNM boundary conditions, á la Leaver [2]. Recently a new method for obtaining analytic/numerical solutions of second order ordinary differential equations with bound potentials has been developed called the asymptotic iteration method (AIM) [3], which was found to be closely connected to continued fractions developed from exact WKB solutions, see reference [4] and those listed in therein. 1 In this article we will demonstrate that the AIM can also be applied to the case of black hole QNMs, which have unbounded (scattering) like potentials.…”

Section: Introductionmentioning

confidence: 99%

“…Note that this is opposite to the case presented in reference[15], where they define the QNMs as solutions with boundary conditions: ψ(x) ∝ e ∓iωx as x → ±∞, cf. equation(4), for e iωt time dependence.…”

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confidence: 99%

Black hole quasinormal modes using the asymptotic iteration method

Cho¹,

Cornell²,

Doukas³

et al. 2010

Class. Quantum Grav.

112

146

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In this article we show that the asymptotic iteration method (AIM) allows one to numerically find the quasinormal modes of Schwarzschild and Schwarzschild de Sitter (SdS) black holes. An added benefit of the method is that it can also be used to calculate the Schwarzschild anti-de Sitter (SAdS) quasinormal modes for the case of spin zero perturbations. We also discuss an improved version of the AIM, more suitable for numerical implementation. ¶ Main address from 1st of June. 1 The phrase "continued fraction" used for WKB solutions should not be confused with the type of continued fractions developed from Frobenius series for QNMs by Leaver [2]. In the rest of the paper "continued fraction" will mean those generated from Frobenius series.

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“…The AIM provides a simple approach to obtaining eigenvalues of bound state problems, even for spheroidal harmonics with c a general complex number, large or small [2,3]. It has also been shown that the AIM is closely related to the continued fractions method (CFM) [4] derived from an exact solution to the Schrödinger equation via a WKB ansatz [5]. A related CFM is often employed in numerical calculations of spheroidal eigenvalues and quasinormal modes of black hole equations [6], which is based on the series solution method of the Hydrogen molecule ion by Jaffé (and generalised by Baber and Hassé) [7].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic iteration method for spheroidal harmonics of higher-dimensional Kerr-(A)dS black holes

et al. 2009

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In this work we calculate the angular eigenvalues of the (n + 4)-dimensional simply rotating Kerr-(A)dS spheroidal harmonics using the Asymptotic Iteration Method (AIM). We make some comparisons between this method and that of the Continued Fraction Method (CFM) and use the latter to check our results. We also present analytic expressions for the small rotation limit up to O(c 3 ) with the coefficient of each power up to O(α 2 ), where c = aω and α = a 2 Λ (a is the angular velocity, ω the frequency and Λ the cosmological constant). 1 Unlike the asymptotically flat limit (Λ = 0) which only has three regular singular points. 2 Of course some manipulation is first required to put the equation into the AIM form.

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A connection between the asymptotic iteration method and the continued fractions formalism

Cited by 8 publications

References 15 publications

Quasi-normal modes of spin-3/2 fields in $D$-dimensional Reissner-Nordström black hole spacetimes using the continued fraction method

Quasi-normal modes of spin-3/2 fields in $D$-dimensional Reissner-Nordström black hole spacetimes using the continued fraction method

Black hole quasinormal modes using the asymptotic iteration method

Asymptotic iteration method for spheroidal harmonics of higher-dimensional Kerr-(A)dS black holes

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