Near-Horizon Conformal Symmetry and Black Hole Entropy

TL;DR

The paper addresses whether the universality of black hole entropy can be explained by a symmetry near the horizon. Using two-dimensional dilaton gravity, the paper derives a chiral Virasoro algebra governing horizon degrees of freedom, with a calculable central charge $c$, and shows that Cardy’s formula reproduces the Bekenstein-Hawking entropy. The central charge and the entropy depend only on near-horizon data, supporting a universal mechanism for black hole thermodynamics. This work thus links horizon conformal symmetry to microscopic counting, offering a path toward quantum gravity insights that are insensitive to the details of the underlying theory.

Abstract

Near an event horizon, the action of general relativity acquires a new asymptotic conformal symmetry. Using two-dimensional dilaton gravity as a test case, I show that this symmetry results in a chiral Virasoro algebra with a calculable classical central charge, and that Cardy's formula for the density of states reproduces the Bekenstein-Hawking entropy. This result lends support to the notion that the universal nature of black hole entropy is controlled by conformal symmetry near the horizon.

Figures (1)

• Figure 1: A black hole spacetime: horizon $\Delta$, two partial Cauchy surfaces $C_1$ and $C_2$, a "reference" cross-section $S$ of $\Delta$, and a neighborhood $\cal N$ of the horizon.