  We investigate the gravitational quasi-normal modes (QNMs) for a type of
regular black hole (BH) known as phantom BH, which is a static self-gravitating
solution of a minimally coupled phantom scalar field with a potential. The
studies are carried out for three different spacetimes: asymptotically flat, de
Sitter (dS), and anti de Sitter (AdS). In order to consider the standard odd
parity and even parity of gravitational perturbations, the corresponding master
equations are derived. The QNMs are discussed by evaluating the temporal
evolution of the perturbation field which, in turn, provides direct information
on the stability of BH spacetime. It is found that in asymptotically flat, dS
and AdS spacetimes, the gravitational perturbations have similar
characteristics for both odd and even parities. The decay rate of perturbation
is strongly dependent on the scale parameter $b$, which measures the coupling
strength between phantom scalar field and the gravity. Furthermore, through the
analysis of Hawking radiation, it is shown that the thermodynamics of such
regular phantom BH is also influenced by $b$. The obtained results might shed
some light on the quantum interpretation of QNM perturbation.
