Near-horizon conformal structure of black holes

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 con tains an inverse square interaction term. It is shown that the operators ap pearing in the corresponding algebraic description belong to the representa tion space of the Virasoro algebra. The operator H is studied using the rep resentation theory of the Virasoro algebra. We observe that the wave functi ons exhibit scaling behaviour in a band-like region near the horizon of the black hole. (C) 2001 Elsevier Science B.V. All rights reserved.