Conformal Enhancement of Holographic Scaling in Black Hole Thermodynamics: A Near-Horizon Heat-Kernel Framework

Standard thermodynamic treatments of quantum field theory in the presence of black-hole backgrounds reproduce the black hole entropy by usually specializing to the leading order of the heat-kernel or the high-temperature expansion. By contrast, this work develops a hybrid framework centered on geometric spectral asymptotics whereby these assumptions are shown to be unwarranted insofar as black hole thermodynamics is concerned. The approach--consisting of the concurrent use of near-horizon and heat-kernel asymptotic expansions--leads to a proof of the holographic scaling of the entropy as a universal feature driven by conformal quantum mechanics.