Conformal Tightness of Holographic Scaling in Black Hole Thermodynamics

TL;DR

This paper demonstrates that the conformal symmetry near black hole horizons is essential for the holographic scaling of scalar-field entropy, revealing a fundamental link between symmetry and black hole thermodynamics.

Contribution

It shows that conformal SO(2,1) invariance is crucial for holographic entropy scaling in black holes, connecting symmetry with thermodynamic properties.

Findings

Conformal symmetry is necessary for holographic entropy scaling.

Radial and angular degrees of freedom contribute multiplicatively to entropy.

Holographic scaling is robust due to conformal invariance and area proportionality.

Abstract

The near-horizon conformal symmetry of nonextremal black holes is shown to be a mandatory ingredient for the holographic scaling of the scalar-field contribution to the black hole entropy. This conformal tightness is revealed by semiclassical first-principle scaling arguments through an analysis of the multiplicative factors in the entropy due to the radial and angular degrees of freedom associated with a scalar field. Specifically, the conformal SO(2,1) invariance of the radial degree of freedom conspires with the area proportionality of the angular momentum sums to yield a robust holographic outcome.