Phase transitions and quasinormal modes of Euler-Heisenberg-dilaton AdS black holes

In this paper, we study phase transitions and scalar quasinormal modes(QNMs) of magnetically charged Euler–Heisenberg-dilaton AdS black holes in the extended phase space. We classify the horizon structures for all three signs of the EH coupling and derive the extended first law when the pressure and coupling are varied. For negative coupling, the physical branch exhibits a Van der Waals-like small/large black-hole transition. Using the improved asymptotic iteration method, we find two separated QNM trajectories below the critical pressure, whereas they merge into one continuous curve at the critical point. The GHS limit and the positive couplings considered here do not produce a finite-radius critical point.