New results for electromagnetic quasinormal and quasibound modes of Kerr black holes

Staicova, Denitsa; Fiziev, P. P.

doi:10.1007/s10509-015-2398-0

Cited by 12 publications

(4 citation statements)

References 103 publications

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“…Other papers on general relativity written in 2015 also include New results for electromagnetic quasinormal and quasibound modes of Kerr black holes, by D.Staicova and P.Fiziev [116], where the authors solve Teukolsky equations with confluent Heun solutions numerically. In Heun functions describing fermions evolving in paralel and magnetic fields, by C. Dariescu and M.A.…”

Section: Some Examples Of the Heun Equation In Physical Applicationsmentioning

confidence: 99%

Heun Functions and Some of Their Applications in Physics

Hortaçsu

2018

Advances in High Energy Physics

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Most of the theoretical physics known today is described by using a small number of differential equations. For linear systems, different forms of the hypergeometric or the confluent hypergeometric equations often suffice to describe the system studied. These equations have power series solutions with simple relations between consecutive coefficients and/ or can be represented in terms of simple integral transforms. If the problem is nonlinear, one often uses one form of the Painlevé equations. There are important examples, however, where one has to use higher order equations. Heun equation is one of these examples, which recently is often encountered in problems in general relativity and astrophysics. Its special and confluent forms take names as Mathieu, Lamé and Coulomb spheroidal equations. For these equations whenever a power series solution is written, instead of a two way recursion relation between the coefficients in the series, we find one between three or four different ones. An integral transform solution using simpler functions also is not obtainable.The use of this equation in physics and mathematical literature exploded in the later years, more than doubling the number of papers with these solutions in the last decade, compared to time period since this equation was introduced in 1889 up to 2008. We use SCI data to conclude this statement, which is not precise, but in the correct ballpark. Here this equation will be introduced and examples for its use, especially in general relativity literature will be given. * This paper is a revised and many times updated version of the conference talk by the same author, published in

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Section: Some Examples Of the Heun Equation In Physical Applicationsmentioning

confidence: 99%

Heun Functions and Some of Their Applications in Physics

Hortaçsu

2018

Advances in High Energy Physics

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“…Details on the boundary conditions, as well as on the whole approach and the explicit values of the parameters, can be found in [1,2,3,7,4,8,9]. In brief, we require:…”

Section: Boundary Conditionsmentioning

confidence: 99%

The Heun Functions and Their Applications in Astrophysics

Staicova

Fiziev²

2016

Springer Proceedings in Mathematics &Amp; Statistics

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“…The general form of the angular Teukolsky equation also named as the spin-weighed spheroidal wave equation has played an important role in the study of black holes with the gravitational self-force [1][2][3][4], quasi-normal modes [5][6][7][8], etc.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions to the angular Teukolsky equation with s ≠ 0

Chen¹,

Wang²,

You³

et al. 2022

Commun. Theor. Phys.

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We first convert the angular Teukolsky equation under the special condition of τ ≠ 0, s ≠ 0, m = 0 into a confluent Heun differential equation (CHDE) by taking different function transformation and variable substitution. And then according to the characteristics of both CHDE and its analytical solution expressed by a confluent Heun function (CHF), we find two linearly dependent solutions corresponding to the same eigenstate, from which we obtain a precise energy spectrum equation by constructing a Wronskian determinant. After that, we are able to localize the positions of the eigenvalues on the real axis or on the complex plane when τ is a real number, a pure imaginary number, and a complex number, respectively and we notice that the relation between the quantum number l and the spin weight quantum number s satisfies the relation l = |s|+ n, n = 0, 1, 2 ∙∙∙. The exact eigenvalues and the corresponding normalized eigenfunctions given by the CHF are obtained with the aid of Maple. The features of the angular probability distribution (APD) and the linearly dependent characteristics of two eigenfunctions corresponding to the same eigenstate are discussed. We find that for a real number τ, the eigenvalue is a real number and the eigenfunction is real function, and the eigenfunction system is an orthogonal complete system, and the APD is asymmetric in the northern and southern hemispheres. For a pure imaginary number τ, the eigenvalue is still a real number and the eigenfunction is a complex function, but the APD is symmetric in the northern and southern hemispheres. When τ is a complex number, the eigenvalue is a complex number, the eigenfunction is still a complex function, and the APD in the northern and southern hemispheres is also asymmetric.

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New results for electromagnetic quasinormal and quasibound modes of Kerr black holes

Cited by 12 publications

References 103 publications

Heun Functions and Some of Their Applications in Physics

Heun Functions and Some of Their Applications in Physics

The Heun Functions and Their Applications in Astrophysics

Exact solutions to the angular Teukolsky equation with s ≠ 0

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