Geodesic Structure, Thermodynamics and Scalar Perturbations of Mod(A)Max black hole Surrounded by Perfect Fluid Dark Matter

Abstract: In this work, we investigate the optical properties of a spherically symmetric Mod(A)Max black hole surrounded by perfect fluid dark matter, focusing on key features such as the photon sphere radius, shadow, photon trajectories, and the effective radial force experienced by photons. We also study the dynamics of massive particles around the black hole, deriving the effective potential and, from it, the specific energy and angular momentum of particles moving in circular orbits of fixed radii is discussed. The conditions for marginally stable circular orbits are analyzed, highlighting how the geometric parameters that modify the spacetime curvature influence both the optical and dynamical features. Furthermore, we explore the thermodynamic behavior of the black hole by examining its temperature, Gibbs free energy, and heat capacity, as well as its thermodynamic topology. Finally, scalar field perturbations are considered through the massless Klein-Gordon equation, and the quasinormal modes (QNMs) in the eikonal regime are computed, illustrating how the geometric parameters affect the potential and the QNM spectra.