Quasinormal modes from potentials surrounding the charged dilaton black hole

Understand

We clarify the purely imaginary quasinormal frequencies of a massless scalar perturbation on the 3D charged-dilaton black holes.

• This case is quite interesting because the potential-step appears outside the event horizon similar to the case of the electromagnetic perturbations on the large Schwarzschild-AdS black holes.
• It turns out that the potential-step type provides the purely imaginary quasinormal frequencies, while the potential-barrier type gives the complex quasinormal modes.