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Geometric warping as a control parameter in extremal dilaton black hole thermodynamics and holography
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DOI：10.1016/j.aop.2026.170620.png)
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Abstract
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We investigate extremal black holes in four-dimensional Einstein–Maxwell–Dilaton gravity with a power-law warped angular sector R(r)=(r/r0)N , where N∈(−1,0) serves as geometric deformation parameter that systematically modifies horizon structure and thermodynamic scaling. Using Wald’s formalism, we derive the exact macroscopic entropy and compute one-loop logarithmic corrections via the heat-kernel expansion, explicitly accounting for regularization-scheme dependence and the warped dilaton-dressed measure. The near-horizon limit yields a universal AdS2×S2 geometry. By imposing explicit boundary conditions and employing the covariant phase space method, we rigorously derive the dual CFT central charge and demonstrate that the Cardy formula exactly reproduces the macroscopic entropy, with the Frolov–Thorne temperature naturally fixing the Virasoro normalization without ad hoc assumptions. Third-order WKB quasinormal mode spectra are evaluated numerically across the parameter space, confirming linear stability and quantitatively showing how N tunes the effective potential barrier and ringdown damping, with results validated against the RN-AdS benchmark. In the extended phase space, we present P – V isotherms and heat capacity profiles that map N -dependent shifts in Davies points and critical coordinates, preserving mean-field universality while revealing distinct thermodynamic regimes at N=−1/2 and N=−3/4 . The model rigorously reduces to the Reissner–Nordström–AdS black hole as N,α→0 in all sectors, establishing geometric warping as a well-defined control parameter for holographic thermodynamics and black hole stability analysis.
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