KONOPLYA, Roman, Olexandr ZHYDENKO and Antonina Frantsivna ZINHAILO. Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations. Classical and Quantum Gravity. 2019, vol. 36, No 15, p. "155002-1"-"155002-26", 26 pp. ISSN 0264-9381. Available from: https://dx.doi.org/10.1088/1361-6382/ab2e25.
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Basic information
Original name Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations
Authors KONOPLYA, Roman (804 Ukraine, guarantor, belonging to the institution), Olexandr ZHYDENKO (804 Ukraine, belonging to the institution) and Antonina Frantsivna ZINHAILO (804 Ukraine, belonging to the institution).
Edition Classical and Quantum Gravity, 2019, 0264-9381.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10308 Astronomy
Country of publisher United Kingdom of Great Britain and Northern Ireland
Confidentiality degree is not subject to a state or trade secret
WWW URL
RIV identification code RIV/47813059:19240/19:A0000430
Organization unit Faculty of Philosophy and Science in Opava
Doi http://dx.doi.org/10.1088/1361-6382/ab2e25
UT WoS 000475394100002
Keywords in English quasinormal modes; WKB method; grey-body factors
Tags FÚ, GA19-03950S, RCTPA, RIVOK, SGS12-2019
Tags International impact, Reviewed
Links GA19-03950S, research and development project.
Changed by Changed by: Ing. Petra Skoumalová, učo 50554. Changed: 21/4/2020 10:31.
Abstract
The WKB approach for finding quasinormal modes of black holes, suggested in Schutz and Will (1985 Astrophys. J. Lett. 291 L33-6) by Schutz and Will at the first order and later developed to higher orders (Iyer and Will 1987 Phys. Rev. D 35 3621; Konoplya 2003 Phys. Rev. D 68 024018; Matyjasek and Opala 2017 Phys. Rev. D 96 024011), 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 Pade approximations, suggested first by Matyjasek and Opala (2017 Phys. Rev. D 96 024011), leads to much higher accuracy of the WKB approach, estimate the error and present the automatic code (The Mathematica (R) package with the WKB formula of 13th order and Pade approximations ready for calculation of the quasinormal modes and grey-body factors, as well as examples of such calculations for the Schwarzschild black hole are publicly available to download from https://goo.gl/nykYGL) which computes quasinormal modes and grey-body factors.
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