  We study separatively the quasinormal modes (QNM) of electromagnetic
perturbations around three-dimensional anti-de Sitter(AdS) black holes in
Jordan and Einstein frames, which are related by the conformal transformations
and a redefinition of a scalar field. We find that, in the Jordan frame, the
imaginary parts of QNM frequencies can reflect the thermodynamical stabilities
of hairy black holes, including the possible phase transition between the hairy
black hole and BTZ black hole, disclosed by examining the corresponding free
energies. Similar results are also uncovered in the Einstein frame. The
obtained results further support that the QNM can be a dynamic probe of the
thermodynamic properties in black holes.
