Hybrid Black Hole Geometry with Lorentz-Violating Quintessential Fields: Thermodynamics, Photon Dynamics, and Perturbative Potentials

In this work, we investigate the optical and thermodynamic properties of an effective hybrid regular black-hole geometry endowed with Lorentz-violating hair and surrounded by a quintessence-like field. The modified metric incorporates a regularizing term associated with Lorentz-symmetry breaking, whose effects are examined through the behavior of the ADM mass, Hawking temperature, Gibbs free energy, and heat capacity. Our analysis reveals significant modifications to the near-horizon structure, thermal stability, and phase-transition patterns, including the emergence of swallow tail-like signatures in the free energy and shifted divergence points in the specific heat. The results show that Lorentz-violating effects, together with the electric charge, string cloud density, and quintessence state parameter, play a decisive role in determining the physical characteristics and thermodynamic phases of the system. These findings provide new insights into black hole phenomenology within extended gravitational frameworks and highlight the interplay between fundamental symmetry breaking and effective matter fields.