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Extracting Data from Behind Horizons with the AdS/CFT Correspondence

Jared Kaplan

Abstract

Recent work has shown that boundary correlators in AdS-Schwarzschild can probe the geometry near the singularity. In this paper we aim to analyze the specific signatures of the singularity, show how significant they can be, and uncover the origins of these large effects in explicitly outside the horizon descriptions. We add perturbations to the metric localized near the singularity and explore their effects on the boundary correlators. Then we use analyticity arguments to show how this information arises from the Euclidean path integral of a free scalar field in the bulk.

Extracting Data from Behind Horizons with the AdS/CFT Correspondence

Abstract

Recent work has shown that boundary correlators in AdS-Schwarzschild can probe the geometry near the singularity. In this paper we aim to analyze the specific signatures of the singularity, show how significant they can be, and uncover the origins of these large effects in explicitly outside the horizon descriptions. We add perturbations to the metric localized near the singularity and explore their effects on the boundary correlators. Then we use analyticity arguments to show how this information arises from the Euclidean path integral of a free scalar field in the bulk.

Paper Structure

This paper contains 11 sections, 49 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Spacetime Geometry
  3. Some $D=3$ Examples
  4. Model Stringy Effects in $D = 5$
  5. Perturbations and Power Series
  6. Path Integral Treatment
  7. Conclusions

Figures (1)

  • Figure 1: This figure shows the Penrose diagram for the $D=3$ AdS-Schwarzschild spacetime with a symmetric spacelike geodesic passing near the singularity. The $D=5$ case has a similar diagram, with one important difference - the singularities must 'bend outward', as shown in fhks.