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Virasoro hair and entropy for axisymmetric Killing horizons

Lin-Qing Chen, Wan Zhen Chua, Shuwei Liu, Antony J. Speranza, Bruno de S. L. Torres

TL;DR

The paper demonstrates that the near-horizon region of generic bifurcate, axisymmetric Killing horizons carries a full 2D conformal symmetry with Virasoro central charges linked to the horizon area. By constructing conformal coordinates that reveal an AdS3 factor and computing the corresponding Virasoro algebras, it derives left/right central charges and temperatures, showing that the Cardy entropy matches the Bekenstein-Hawking entropy. Imposing integrability aligns the central charges, and Wald–Zoupas flux terms further support a universal, area-proportional central charge under general conditions, strengthening the claim of a holographic CFT description of horizon microstates. The results motivate exploring horizon holography across a broad class of horizons, including de Sitter and higher-dimensional cases, and raise questions about fixing the auxiliary parameters and the role of edge modes in black hole thermodynamics.

Abstract

We show that the gravitational phase space for the near-horizon region of a bifurcate, axisymmetric Killing horizon in any dimension admits a 2D conformal symmetry algebra with central charges proportional to the area. This extends the construction of [Haco et. al., JHEP 12, 098 (2018)] to generic Killing horizons appearing in solutions of Einstein's equations, and motivates a holographic description in terms of a 2D conformal field theory. The Cardy entropy in such a field theory agrees with the Bekenstein-Hawking entropy of the horizon, suggesting a microscopic interpretation.

Virasoro hair and entropy for axisymmetric Killing horizons

TL;DR

The paper demonstrates that the near-horizon region of generic bifurcate, axisymmetric Killing horizons carries a full 2D conformal symmetry with Virasoro central charges linked to the horizon area. By constructing conformal coordinates that reveal an AdS3 factor and computing the corresponding Virasoro algebras, it derives left/right central charges and temperatures, showing that the Cardy entropy matches the Bekenstein-Hawking entropy. Imposing integrability aligns the central charges, and Wald–Zoupas flux terms further support a universal, area-proportional central charge under general conditions, strengthening the claim of a holographic CFT description of horizon microstates. The results motivate exploring horizon holography across a broad class of horizons, including de Sitter and higher-dimensional cases, and raise questions about fixing the auxiliary parameters and the role of edge modes in black hole thermodynamics.

Abstract

We show that the gravitational phase space for the near-horizon region of a bifurcate, axisymmetric Killing horizon in any dimension admits a 2D conformal symmetry algebra with central charges proportional to the area. This extends the construction of [Haco et. al., JHEP 12, 098 (2018)] to generic Killing horizons appearing in solutions of Einstein's equations, and motivates a holographic description in terms of a 2D conformal field theory. The Cardy entropy in such a field theory agrees with the Bekenstein-Hawking entropy of the horizon, suggesting a microscopic interpretation.

Paper Structure

This paper contains 11 sections, 58 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Near-horizon expansion
  3. Central charges
  4. Temperature and Entropy
  5. Wald-Zoupas term
  6. Discussion
  7. Near-horizon coordinates
  8. de Sitter example
  9. Kerr example
  10. Computation of central charge
  11. Wald-Zoupas term

Figures (1)

  • Figure 1: Plot of the bifurcate Killing horizon (yellow) with three spirals depicting intersections of constant $w^+, w^-$. From top to bottom, they correspond to $w^+/w^- = (5, 1, 1/5)$, with the same value of the product $w^+ w^-$. They penetrate into any fixed-$x$ hyperbola, shown in light brown, at the same $y$. The arrows indicate the direction of increasing $y$ on approaching the bifurcation surface.