Near-Horizon Conformal Structure and Entropy of Schwarzschild Black Holes

TL;DR

This paper investigates the near-horizon conformal structure of Schwarzschild black holes using a scalar probe, revealing a Virasoro algebra connection and deriving the Bekenstein-Hawking entropy with a specific logarithmic correction.

Contribution

It demonstrates the emergence of a Virasoro algebra and scaling behavior in near-horizon dynamics, providing a conformal field theory perspective on black hole entropy.

Findings

Virasoro algebra governs near-horizon dynamics.

Wavefunctions exhibit scaling behavior near the horizon.

Entropy includes a -3/2 log M^2 correction term.

Abstract

Near-horizon conformal structure of a massive Schwarzschild black hole of mass M is analyzed using a scalar field as a simple probe of the background geometry. The near-horizon dynamics is governed by an operator which is related to the Virasoro algebra and admits a one-parameter family of self-adjoint extensions described by a real parameter z. When z satisfies a suitable contraint, the corresponding wavefunctions exhibit scaling behaviour in a band-like region near the horizon of the black hole. This formalism is consistent with the Bekenstein-Hawking entropy formula and naturally produces the -3/2 log M^2 correction term to the black hole entropy with other subleading corrections exponentially suppressed. This precise form for the black hole entropy is expected on general grounds in any conformal field theoretic description of the problem. The presence of the Virasoro algebra and the scaling properties of the associated wavefunctions in the near-horizon region together with the appearance of the logarithmic correction to the Bekenstein-Hawking entropy provide strong evidence for the near-horizon conformal structure in this system.