Conformal description of horizon's states

TL;DR

This paper formulates a conformal field theory description of black hole horizons, deriving a Virasoro algebra with a central charge proportional to entropy, and matches the Bekenstein-Hawking entropy via Cardy's formula.

Contribution

It introduces a universal two-dimensional conformal theory at the horizon for any dimension d≥3, connecting horizon symmetries to the Virasoro algebra and black hole entropy.

Findings

Virasoro algebra with central charge proportional to entropy

Effective 2D conformal theory at the horizon

Matching of entropy via Cardy's formula

Abstract

The existence of black hole horizon is considered as a boundary condition to be imposed on the fluctuating metrics. The coordinate invariant form of the condition for class of spherically symmetric metrics is formulated. The diffeomorphisms preserving this condition act in (arbitrary small) vicinity of the horizon and form the group of conformal transformations of two-dimensional space ($r-t$ sector of the total space-time). The corresponding algebra recovered at the horizon is one copy of the Virasoro algebra. For general relativity in $d$ dimensions we find an effective two-dimensional theory governing the conformal dynamics at the horizon universally for any $d\geq 3$. The corresponding Virasoro algebra has central charge $c$ proportional to the Bekenstein-Hawking entropy. Identifying the zero-mode configuration we calculate $L_0$. The counting of states of this horizon's conformal field theory by means of Cardy's formula is in complete agreement with the Bekenstein-Hawking expression for the entropy of black hole in $d$ dimensions.