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AdS black holes as reflecting cavities

Irene Amado, Carlos Hoyos-Badajoz

TL;DR

The paper develops a geometric, high-frequency framework to connect bulk causal structure in AdS black holes with the analytic structure of time-dependent thermal Green functions in the dual field theory. By employing the eikonal approximation, it treats bulk propagation as null rays that reflect off the AdS boundary and singularities, yielding a reflecting-cavity picture and linking boundary singularities to ultraviolet bulk dynamics. It derives an explicit, universal expression for the asymptotic quasinormal frequencies, omega_n, in large AdS black holes and explains their time-domain counterparts as a sequence of singularities t_n in complex time. This approach provides a topological, geometric understanding of holographic correlators and offers a pathway to generalize to other black hole geometries and to inverse holography, while highlighting the role of SK formalism and potential quantum corrections.

Abstract

We use the identification between null singularities of correlators in the bulk with time singularities in the boundary correlators to study the analytic structure of time-dependent thermal Green functions using the eikonal approximation for classical solutions in the AdS black hole background. We show that the location of singularities in complex time can be understood in terms of null rays bouncing on the boundaries and singularities of the eternal black hole, giving the picture of a `reflecting cavity'. We can then extract the general analytic expression for the asymptotic values of the frequencies of quasinormal modes in large AdS black holes.

AdS black holes as reflecting cavities

TL;DR

The paper develops a geometric, high-frequency framework to connect bulk causal structure in AdS black holes with the analytic structure of time-dependent thermal Green functions in the dual field theory. By employing the eikonal approximation, it treats bulk propagation as null rays that reflect off the AdS boundary and singularities, yielding a reflecting-cavity picture and linking boundary singularities to ultraviolet bulk dynamics. It derives an explicit, universal expression for the asymptotic quasinormal frequencies, omega_n, in large AdS black holes and explains their time-domain counterparts as a sequence of singularities t_n in complex time. This approach provides a topological, geometric understanding of holographic correlators and offers a pathway to generalize to other black hole geometries and to inverse holography, while highlighting the role of SK formalism and potential quantum corrections.

Abstract

We use the identification between null singularities of correlators in the bulk with time singularities in the boundary correlators to study the analytic structure of time-dependent thermal Green functions using the eikonal approximation for classical solutions in the AdS black hole background. We show that the location of singularities in complex time can be understood in terms of null rays bouncing on the boundaries and singularities of the eternal black hole, giving the picture of a `reflecting cavity'. We can then extract the general analytic expression for the asymptotic values of the frequencies of quasinormal modes in large AdS black holes.

Paper Structure

This paper contains 7 sections, 50 equations, 2 figures.

Table of Contents

  1. Introduction
  2. AdS with a mirror
  3. The eikonal approximation in AdS black holes
  4. Matching of eikonal solutions and bouncing rays
  5. Black holes as reflecting cavities
  6. Discussion
  7. Acknowledgments:

Figures (2)

  • Figure 1: Null geodesic bouncing on and off from the boundary at $z=0$ and the mirror surface at $z=z_0$.
  • Figure 2: Kruskal diagram of a eternal black hole in AdS space. The light solid line represents a null geodesic starting on the boundary at $t=0$ bouncing on the future singularity, on the second AdS boundary, on the past singularity and back to the boundary at $t=(\cot\frac{\pi}{d}-i)\beta$.