Dynamical Evolution of a Scalar Field Coupling to Einstein’s Tensor in Charged Braneworld Black Holes

Abstract

In this work, we study the quasinormal modes (QNMs) of scalar field coupling to Einstein’s tensor in charged braneworld black hole. The shape of the potential function is illustrated and we find that lower coupling constant leads to more stable field. We then apply six-order WKB approximation to calculate the quasinormal frequencies (QNF) in weaker coupling field, and depict the dependence of the oscillation frequency on the coupling constant. Furthermore, we use finite difference method to shape the evolution of the coupling field and find that coupling field with lower multipole numbers l corresponds to stable field, while higher l tends to lead to instability when the coupling constant is larger than a threshold value. Finally the fitting curve of such threshold value is given numerically.