Gravitational quasi-normal modes of static R2 Anti-de Sitter black holes**Project supported by the National Natural Science Foundation of China (Grant Nos. 11205254, 11178018, 11375279, and 11605015), the Fundamental Research Funds for the Central Universities, China (Grant Nos. 106112016CDJXY300002 and CDJRC10300003), the Chinese State Scholarship Fund, FAPESP (Grant No. 2012/08934-0), and the Natural Science Foundation Project of CQ CSTC (Grant No.

Abstract

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 of the QNMs increase together as increases for a given angular momentum number l. That indicates with a larger value of 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.