Quasinormal modes response to thermodynamic phase transitions in the charged AdS black hole surrounded by perfect fluid dark matter
We investigate how thermodynamic phase transitions are reflected in the quasinormal modes (QNMs) of charged anti-de Sitter (AdS) black holes surrounded by perfect fluid dark matter (PFDM). In the extended phase space, increasing the positive PFDM parameter raises the critical temperature and pressure while reducing the critical horizon radius. We compute the fundamental QNMs of a massless scalar perturbation using a Chebyshev pseudospectral method and analyze their evolution along isobaric and isothermal processes below the critical point. The small and large black hole branches trace clearly separated QNM trajectories and display sharply different slopes near the first-order transition, providing a dynamical signature of the branch change. Along isotherms, this evolution results from the competing effects of the horizon radius and pressure, or equivalently the AdS radius, rather than from the horizon radius alone. At the critical point, however, the QNM frequencies vary smoothly with the horizon radius and show no sharp signature of the second-order transition. Along the coexistence curve, the separation between the small and large black hole QNMs decreases as the Gibbs free energy swallowtail shrinks and vanishes at criticality. These results show that PFDM shifts both the thermodynamic phase structure and the associated QNM response, while the fundamental scalar QNM spectrum remains sensitive to the first-order small/large black hole transition.