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

TL;DR

This paper introduces a hybrid geometric spectral asymptotics framework that demonstrates the holographic scaling of black hole entropy, emphasizing the role of conformal quantum mechanics beyond traditional heat-kernel approximations.

Contribution

It develops a novel near-horizon heat-kernel framework that proves the universality of holographic entropy scaling in black hole thermodynamics.

Findings

Holographic entropy scaling is a universal feature.

Traditional heat-kernel methods are insufficient for full thermodynamic descriptions.

Conformal quantum mechanics underpins the entropy behavior.

Abstract

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.