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.