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Physics Seminar Date: Wednesday, 12 February 2025 Time: 1.45 PM Venue: Lecture Hall 2 Thermodynamics of topological Dyonic hairy black holes and interplay of QNMs at the phase transition Supragyan Priyadarshinee IISER, Mohali. 12-02-25 Abstract We present and discuss a new family of topological hairy dyonic black hole solutions in asymptotically anti–de Sitter space. The coupled Einstein-Maxwell-scalar gravity system, that carries both the electric and magnetic charges is solved, and exact hairy dyonic black hole solutions are obtained analytically. The scalar field profiles that give rise to such black hole solutions are regular everywhere. The hairy solutions are obtained for planar, spherical, and hyperbolic horizon topologies. In addition, analytic expressions of regularized action, stress tensor, conserved charges, and free energies are obtained. We further comment on different prescriptions for computing the black hole mass with hairy backgrounds. We analyze the thermodynamics of these hairy dyonic black holes in canonical and grand canonical ensembles, and we find that both electric and magnetic charges have a constructive effect on the stability of the hairy solution. For the case of planar and hyperbolic horizons, we find thermodynamically stable hairy black holes that are favored at low temperatures compared to the nonhairy counterparts. We further find that, for a spherical hairy dyonic black hole, the thermodynamic phase diagram resembles to that of a Van der Waals fluid not only in canonical but also in the grand canonical ensemble. Then, we explore the dynamics of the massless scalar field in the context of hairy black holes at the phase transition, utilizing both the series solution and shooting methods, we numerically compute the corresponding quasinormal modes (QNMs) across various black hole parameters. Notably, the values obtained from these two methods exhibit robust agreement. The consistently negative imaginary part of the QNM underscores the stability of the massless scalar field in the backdrop of the black hole. Our investigation reveals that both the decay and oscillatory modes of the scalar field perturbation exhibit a linear increase with the horizon radius, particularly notable for large black holes. We conduct a comprehensive analysis of QNMs across diverse black hole parameters, encompassing the electric charge, magnetic charge, horizon radius, and the hairy parameter. Moreover, we extend our scrutiny to the QNM behaviour near the small/large black hole phase transition. Intriguingly, we discern distinct characteristics in the nature of QNMs between the large and small black hole phases, indicating the potential of QNMs as a probing tool for black hole phase transitions.
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