Scalar quasinormal modes of nonlinear charged black holes in Rastall gravity

¹ MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF, and School of Physics, Huazhong University of Science and Technology 430074, Wuhan, Hubei, China
² Hubei Subsurface Multi- scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences - 430074, Wuhan, Hubei, China
³ Escola de Engenharia de Lorena, Universidade de São Paulo - 12602810, Lorena, SP, Brazil
⁴ Faculdade de Engenharia de Guaratinguetá, Universidade Estadual Paulista - 12516410, Guaratinguetá, SP, Brazil
⁵ Center for Gravitation and Cosmology, School of Physical Science and Technology, Yangzhou University 225002, Yangzhou, Jiangsu, China

^(a) yjtan@hust.edu.cn
^(b) cgshao@hust.edu.cn
^(c) lk314159@hotmail.com
^(d) wlqian@usp.br

Received: 17 October 2019
Accepted: 9 December 2019

Abstract

In this paper, the scalar quasinormal modes of nonlinear charged black hole metrics in Rastall gravity is investigated. The electromagnetic tensor presented in the background spacetime possesses a power-law form, and the system is assumed to be surrounded by a quintessence field. By utilizing the recently obtained analytic form of the metric, the quasinormal frequencies are obtained via the matrix method. The numerical values have been further compared against those evaluated by using the WKB approximation up to thirteenth order. Also, the finite difference method is utilized to study the temporal evolution of the scalar perturbations. In terms of calculations carried out for both massless and massive scalar fields, we discuss the properties of the resultant quasinormal frequencies, as well as their dependences on the model parameters describing the background black hole. To be specific, the effect of the electric charge, mass of the scalar field, and equation of state of the quintessence are examined. Besides, the quasinormal frequencies associated with an extremal black hole regarding the Nariai limit is explored, where the obtained results are found to be consistent with theoretical arguments. The black hole metric is found to be stable against scalar perturbations, in the presence of both linear and nonlinear electromagnetic fields.