Quasinormal modes of gravitational field perturbation of regular phantom black holes

We study the gravitational quasi-normal modes (QNMs) for a kind of regular black hole named as phantom black hole (BH), which is a solution of a self-gravitating minimally coupled scalar field with an arbitrary potential.The parameter conditions of such BH are investigated in asymptotically flat, de sitter (dS), and anti de sitter (AdS) spacetimes separately. Considering the standard odd parity and even parity of gravitational perturbation, the corresponding master equations are derived and quasi-normal perturbation are discussed in asymptotically flat and dS spacetimes. The dynamic evolution of the perturbation field indicates the stability of gravitational perturbation directly. On the whole in asymptotically flat and dS spacetimes, the gravitational perturbations have the similar characteristics for odd and even parities. The decay speed of perturbation is strongly dependent on the scale $b$. Furthermore through the analysis of Hawking radiation, the thermodynamics of such regular phantom black hole is also influenced by $b$ significantly. This might be hopeful to support a bridge for quantum interpretation of QNMs perturbation.