Quasinormal modes, greybody factors and thermodynamics of four dimensional AdS black holes in Critical Gravity

In the present work, considering critical gravity as a gravity model, an electrically charged topological Anti-de Sitter black hole with a matter source characterized by a nonlinear electrodynamics framework is obtained. This configuration is defined by an integration constant, three key structural constants, and a constant that represents the topology of the event horizon. Additionally, based on the Wald formalism, we probe that this configuration enjoys non-trivial thermodynamic quantities, establishing the corresponding first law of black hole thermodynamics, as well as local stability under thermal and electrical fluctuations. Additionally, via the Gibbs free energy we note that the topology of the base manifold allows us to compare this charged configuration with respect to the thermal AdS space-time, allowing us to obtain a first-order phase transition. The quasinormal modes and the greybody factor are also calculated by considering the spherical situation. We found that the quasinormal modes exhibit a straightforward change for variations of one of the structural constants.