Black Hole Thermodynamics from Near-Horizon Conformal Quantum Mechanics

TL;DR

This paper demonstrates that black hole thermodynamics can be derived from near-horizon conformal invariance using conformal quantum mechanics, revealing holographic properties and linking conformal coupling to Hawking temperature.

Contribution

It introduces a novel approach connecting near-horizon conformal symmetry with black hole thermodynamics across general metrics in higher dimensions.

Findings

Reveals holographic properties emerge from near-horizon conformal invariance.

Shows conformal coupling parameter relates to Hawking temperature.

Validates Schwarzschild coordinates for thermodynamic analysis despite singularities.

Abstract

The thermodynamics of black holes is shown to be directly induced by their near-horizon conformal invariance. This behavior is exhibited using a scalar field as a probe of the black hole gravitational background, for a general class of metrics in D spacetime dimensions (with $D \geq 4$). The ensuing analysis is based on conformal quantum mechanics, within a hierarchical near-horizon expansion. In particular, the leading conformal behavior provides the correct quantum statistical properties for the Bekenstein-Hawking entropy, with the near-horizon physics governing the thermodynamic properties from the outset. Most importantly: (i) this treatment reveals the emergence of holographic properties; (ii) the conformal coupling parameter is shown to be related to the Hawking temperature; and (iii) Schwarzschild-like coordinates, despite their ``coordinate singularity,''can be used self-consistently to describe the thermodynamics of black holes.