Near-Horizon Conformal Symmetry and Black Hole Entropy

TL;DR

This paper demonstrates that near the event horizon of black holes, a conformal symmetry leads to a Virasoro algebra whose associated Cardy formula accurately reproduces the Bekenstein-Hawking entropy, suggesting a universal conformal symmetry role.

Contribution

It shows that near-horizon conformal symmetry in gravity yields a Virasoro algebra with a classical central charge, linking it directly to black hole entropy calculation.

Findings

Virasoro algebra with classical central charge derived near the horizon

Cardy's formula reproduces Bekenstein-Hawking entropy

Supports conformal symmetry as a universal feature of black hole horizons

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.