Quasinormal modes of asymptotically (A)dS black hole in Lovelock background

Abbasvandi, Niloofar; Soleimani, Maliheh; Abdullah, Wan Ahmad Tajuddin Wan; Radiman, Shahidan

doi:10.1088/1475-7516/2017/03/030

Cited by 1 publication

(2 citation statements)

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“…The latter yields that the representation (21) is equivalent to (20) up to the given order k, i. e. the coefficients Q 0 , Q 1 , . .…”

Section: Further Improvement Of the Wkb Formula Accuracymentioning

confidence: 99%

“…In order to increase accuracy of the higher-order WKB formula, it has been recently proposed to use Padé approximants [61] for the usual WKB formula [4]. Within this approach one has to define a polynomial P k (ǫ) by introducing powers of the order parameter ǫ in the righthand side of the WKB formula (17) as follows, (20) where the polynomial order k coincides with the order of the WKB formula. Formal parameter ǫ is introduced in the same way as in [2] in order to keep track of orders in the WKB approximation, and the squared frequency can be obtained by taking ǫ = 1,…”

Section: Further Improvement Of the Wkb Formula Accuracymentioning

confidence: 99%

See 1 more Smart Citation

Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations

Konoplya

Zhidenko

Zinhailo

2019

Class. Quantum Grav.

294

248

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The WKB approach for finding quasinormal modes of black holes, suggested in [1] by Schutz and Will at the first order and later developed to higher orders [2][3][4], became popular during the past decades, because, unlike more sophisticated numerical approaches, it is automatic for different effective potentials and mostly provides sufficient accuracy. At the same time, the seeming simplicity of the WKB approach resulted in appearance of a big number of partially misleading papers, where the WKB formula was used beyond its scope of applicability. Here we review various situations in which the WKB formula can or cannot bring us to reliable conclusions. As the WKB series converges only asymptotically, there is no mathematically strict criterium for evaluation of an error. Therefore, here we are trying to introduce a number of practical recipes instead and summarize cases in which higher WKB orders improve accuracy. We show that averaging of the Padé approximations, suggested first by J. Matyjasek and M. Opala [4], leads to much higher accuracy of the WKB approach, estimate the error and present the automatic code [5] which computes quasinormal modes and grey-body factors. WKB orderPublication 1 B. Mashhoon [8], B. Schutz and C. Will [1] 2-3 S. Iyer and C. Will [2] 4-6 R. Konoplya [3] 7-13 J. Matyjasek and M. Opala [4] 3 0.

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“…The latter yields that the representation (21) is equivalent to (20) up to the given order k, i. e. the coefficients Q 0 , Q 1 , . .…”

Section: Further Improvement Of the Wkb Formula Accuracymentioning

confidence: 99%