Dymnikova Black Hole Immersed in Perfect Fluid Dark Matter and a Cloud of Strings: Hawking Temperature, Dynamics and QPOs Analysis

Abstract: The Dymnikova black hole represents a regular spacetime solution interpolating between a de Sitter core and an asymptotically Schwarzschild geometry. In this work, we investigate a generalized Dymnikova black hole surrounded by perfect fluid dark matter (PFDM) and immersed in a cloud of strings (CS). We analyze how these additional matter sources modify the thermodynamic, optical, and dynamical properties of the spacetime. We derive the Hawking temperature and specific heat capacity and examine the thermal stability and phase structure of the black hole. The results reveal non-monotonic temperature behavior and parameter-dependent phase transitions. We further study photon dynamics, including the photon sphere and black hole shadow, and show that both PFDM and string cloud parameters significantly affect the shadow radius and strong-field structure. Additionally, we investigate the motion of massive test particles, circular orbits, and stability conditions. The corresponding effective potentials, specific energy, and angular momentum are analyzed. Finally, we explore quasi-periodic oscillations (QPOs) by computing the fundamental epicyclic frequencies and discuss how the model parameters encode observable astrophysical signatures.