Frolov-AdS black holes immersed in a string fluid: Harmonic oscillations, phase structure, and topological classification

Abstract

This work examines the thermodynamic topology of Frolov-AdS black holes with a surrounding string fluid, highlighting the role of topological charges in determining stability. By analyzing vector fields constructed from the free energy, we identify zero points corresponding to distinct topological charges, which vary with entropy-related parameters. Our findings demonstrate that the system exhibits topological charges of +1, 0, or-1, serving as a robust criterion for black hole stability classification. Furthermore, we examine photon sphere (PS) configurations, revealing that their associated (PS = -1) reflect underlying geometric and thermodynamic structures of black hole. This study establishes connections between winding numbers and black hole phase transitions. Comparative analyses with classical black holes support the universality of the topological framework. Complementarily, the analysis of quasi-periodic oscillations elucidates the intricate interplay of electric charge, spin, cosmological constant, and string-fluid background on epicyclic and precessional motions around charged AdS black holes. Electric charge diminishes gravitational binding, shifting characteristic frequencies outward, while spin-induced frame dragging enhances orbital stability and periapsis advance. The AdS curvature associated with a negative cosmological constant universally suppresses oscillatory frequencies and modifies periastron dynamics, whereas the string-fluid parameter governs asymptotic decay rates and far-field behavior. These combined effects yield comprehensive predictions for quasinormal mode spectra and potential astrophysical signatures.