Resonant frequencies of linear dilaton black holes in Einstein-Maxwell-Dilaton gravity

Charged massless scalar field perturbations are analyzed in the gravitational, electromagnetic, and dilaton fields of linear dilaton black holes. After separating the covariant Klein–Gordon equation (KGE) into radial and angular parts, we show how one obtain the analytical solutions of the radial equation in terms of the confluent Heun functions. Then, we consider the problems of resonant frequencies and quantization with the help of the obtained radial equation.Charged massless scalar field perturbations are analyzed in the gravitational, electromagnetic, and dilaton fields of linear dilaton black holes. After separating the covariant Klein–Gordon equation (KGE) into radial and angular parts, we show how one obtain the analytical solutions of the radial equation in terms of the confluent Heun functions. Then, we consider the problems of resonant frequencies and quantization with the help of the obtained radial equation.