Detailed Information on Publication Record
2019
Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations
KONOPLYA, Roman, Olexandr ZHYDENKO and Antonina Frantsivna ZINHAILOBasic 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
Language
English
Type of outcome
Článek v odborném periodiku
Field of Study
10308 Astronomy
Country of publisher
United Kingdom of Great Britain and Northern Ireland
Confidentiality degree
není předmětem státního či obchodního tajemství
References:
RIV identification code
RIV/47813059:19240/19:A0000430
Organization unit
Faculty of Philosophy and Science in Opava
UT WoS
000475394100002
Keywords in English
quasinormal modes; WKB method; grey-body factors
Tags
Tags
International impact, Reviewed
Links
GA19-03950S, research and development project.
Změněno: 21/4/2020 10:31, Ing. Petra Skoumalová
Abstract
V originále
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.