We present a comprehensive analytical study of a four-dimensional dilaton black hole with a deformed angular geometry r 2 R(r) 2 , where R(r) = (r/r 0 ) N , coupled to nonlinear electrodynamics and a Liouville-type potential. The model generalizes standard black hole solutions by incorporating a geometric deformation that modifies the horizon structure and thermodynamic behavior. We derive the field equations and compute the Hawking temperature, classical entropy, and quantum-corrected entropy S = S 0 + cln S 0 without resorting to numerical methods. The logarithmic correction coefficient c is explicitly evaluated for generic N and special cases N = −1/2, −3/4, revealing its sensitivity to the dilaton coupling α, charge q, and geometric parameter N. We analyze the limits q → 0 and Λ → 0, showing that quantum corrections persist even in the absence of electromagnetic or cosmological terms, indicating their origin in the modified geometry. Crucially, we demonstrate that in the limit N → 0, α → 0, γ → 0, the solution reduces exactly to the Reissner-Nordström-AdS black hole, with all thermodynamic quantities recovering their standard forms. This confirms the model as a consistent deformation of classical black holes. The results highlight the significant role of geometric and scalar deformations in shaping black hole thermodynamics and quantum properties.
R. Baghbani (Fri,) studied this question.
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