danДоклады Национальной академии наук БеларусиDoklady of the National Academy of Sciences of Belarus1561-83232524-2431The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-8323-2018-62-6-668-673dan-566Research ArticleФИЗИКАPHYSICSКрасное смещение излучения точечного источника, движущегося в поле вращающейся черной дырыRedshift of radiation of a point-like source moving in the external Kerr fieldКомаровС. О.KomarovS. O.

ассистент

Assistant

staskomarov@tut.byГорбацевичА. К.GorbatsievichA. K.

д-р физ.- мат. наук, профессор

D. Sc. (Physics and Mathematics), Professor

gorbatsievich@bsu.byТарасенкоА. Н.TarasenkoA. N.tarasenk@tut.byБелорусский государственный университет, МинскBelarusian State University, Minsk201813012019626668673Copyright © Комаров С.О., Горбацевич А.К., Тарасенко А.Н., 20192019Комаров С.О., Горбацевич А.К., Тарасенко А.Н.Komarov S.O., Gorbatsievich A.K., Tarasenko A.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.belnauka.by/jour/article/view/566

Для точечного источника электромагнитного излучения, движущегося в гравитационном поле вращающейся черной дыры, описываемой метрикой Керра, разработан метод вычисления красного смещения как функции времени удаленного наблюдателя. В отличие от широко представленных в литературе способов, граничная задача для траектории луча решена не численным подбором параметров, а на основе приближенных аналитических выражений для изотропных геодезических в метрике Керра. Предложенный метод проиллюстрирован на примере модельной задачи с параметрами, соответствующими реальным звездам, движущимся в непосредственной близости сверхмассивной черной дыры, находящейся в центре нашей Галактики. На этом же примере показана эффективность и хорошая точность данного метода.

The method of calculation of redshift of light from a point-like source that moves in the gravitational field of the Kerr black hole as a function of time of observation is developed. The widely presented in literature methods for solving the boundary problem are based on a numerical selection of parameters of geodesics. In contrast, the proposed method is based on approximate analytical expressions for isotropic geodesics in the Kerr metric. The proposed method is illustrated by the example of a model problem with parameters corresponding to real stars moving in the immediate vicinity of a supermassive black hole located in the Center of our Galaxy. The same example shows the efficiency and good accuracy of this method.

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The authors declare that there are no conflicts of interest present.