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چکیده
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In this letter, we develop a unified semiclassical framework for the thermodynamics and quantization of the Reissner–Nordström (RN) black hole (BH) based on the Misner–Sharp–Hernandez (MSH) mass. Treating the quasi-local horizon energies as the relevant thermodynamic variables, we formulate a horizon-by-horizon first law and Smarr relation. Using a reduced phase-space quantization, we obtain a discrete MSH mass spectrum for both horizons, which reproduces the minimal entropy spacing. Quantum transitions between adjacent levels yield Planck-scale corrections to the Hawking temperatures and a universal logarithmic contribution to the entropy, consistent with independent approaches to quantum gravity. We encode these corrections into a quantum-deformed RN geometry via a simple multiplicative factor that preserves the classical horizon positions while reproducing the corrected surface gravities. The associated effective stress tensor behaves as a conserved vacuum-polarization source with characteristic 𝑟−4 falloff and a small trace, providing a compact representation of semiclassical backreaction. The deformation slightly lowers both horizon temperatures, weakens the innerhorizon instability, and induces tiny shifts in photon-sphere and shadow observables for macroscopic BHs.
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