Gravitational quasi-normal modes of static R² Anti-de Sitter black holes

In this paper, we study the gravitational quasi-normal modes (QNMs) for a static R² black hole (BH) in Anti-de Sitter (AdS) spacetime. The corresponding master equation of odd parity is derived and the QNMs are evaluated by the Horowitz and Hubeny method. Meanwhile the stability of such BH is also discussed through the temporal evolution of the perturbation field. Here we mainly consider the coefficient λ, which is related to the radius of AdS black hole, on the QNMs of the R² AdS BH. The results show that the Re(ω) and |Im(ω)| of the QNMs increase together as |λ| increases for a given angular momentum number l. That indicates with a larger value of |λ| the corresponding R² AdS BH returns to stable much more quickly. The dynamic evolution of the perturbation field is consistent with the results derived by the Horowitz and Hubeny method. Since in the conformal field theory the QNMs can reflect its approach to equilibrium, so our related results could be referential to studies of the AdS/CFT conjecture. The relationship between λ and the properties of the static R² BH might be helpful for the development of R² gravitational theory.