Near-Horizon Conformal Structure of Black Holes

TL;DR

This paper explores the algebraic structure of black hole horizons, revealing a Virasoro algebra connection and scaling behaviors of scalar fields near the horizon, which may deepen understanding of black hole quantum properties.

Contribution

It demonstrates that near-horizon dynamics can be described using Virasoro algebra representations, linking black hole geometry to conformal field theory structures.

Findings

Operators form a Virasoro algebra representation

Wave functions show scaling behavior near the horizon

Inverse square interaction influences near-horizon dynamics

Abstract

The near-horizon properties of a black hole are studied within an algebraic framework, using a scalar field as a simple probe to analyze the geometry. The operator H governing the near-horizon dynamics of the scalar field contains an inverse square interaction term. It is shown that the operators appearing in the corresponding algebraic description belong to the representation space of the Virasoro algebra. The operator H is studied using the representation theory of the Virasoro algebra. We observe that the wave functions exhibit scaling behaviour in a band-like region near the horizon of the black hole.