Semiclassical Methods in Curved Spacetime and Black Hole Thermodynamics

TL;DR

This paper introduces advanced semiclassical techniques combining conformal quantum mechanics, a generalized WKB framework, and phase-space methods to analyze scalar fields in curved spacetime, deriving black hole thermodynamics from near-horizon conformal invariance.

Contribution

It develops a novel semiclassical approach that unifies multiple methods to better understand black hole thermodynamics from near-horizon conformal symmetry.

Findings

Semiclassical methods are improved and unified.

Black hole thermodynamics is derived from near-horizon conformal invariance.

Approach is asymptotically exact with hierarchical expansions.

Abstract

Improved semiclassical techniques are developed and applied to a treatment of a real scalar field in a $D$-dimensional gravitational background. This analysis, leading to a derivation of the thermodynamics of black holes, is based on the simultaneous use of: (i) a near-horizon description of the scalar field in terms of conformal quantum mechanics; (ii) a novel generalized WKB framework; and (iii) curved-spacetime phase-space methods. In addition, this improved semiclassical approach is shown to be asymptotically exact in the presence of hierarchical expansions of a near-horizon type. Most importantly, this analysis further supports the claim that the thermodynamics of black holes is induced by their near-horizon conformal invariance.