The Stability Of The Charged Spherically Symmetric Black Holes In F(R) Grivity

Recently,a novel class of charged spherically symmetric black hole solutions in f(R)gravity has been derived.Our goal is to explore the stability of such black holes under the perturbations of external scalar fields.Firstly,we consider the perturbations of the neutral massless scalar field.We calculate the quasinormal modes with the third-order WKB method in the frequency-domain and numerically investigate the profiles of the perturbations with Finite-Difference in Time-Domain.Through the calculation of the quasinormal modes,it can be determined that the black hole space-time is stable,and we find that as the black hole parameter a increase,the black hole perturbations decay faster,so the black hole stability is better.Then,we investigate the perturbations of the charged massive scalar field that may trigger the superradiant instability.We express the effective potential in the form of a polynomial and use algebraic methods to analytically prove that when the the frequency of the scalar field satisfies the superradiant condition and the bound-state boundary condition 0<?<min(?),the effective potential of the perturbation equation cannot form a potential well.Therefore,there is no superradiant instability in the novel charged black holes.