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Holography beyond the horizon and cosmic censorship

Thomas S. Levi, Simon F. Ross

TL;DR

This work extends the Kraus-Ooguri-Shenker analytic-continuation program to rotating BTZ black holes in AdS/CFT, addressing how physics behind the event horizon is encoded in the boundary theory. Using bulk-boundary propagators built by the image method and a Euclidean-to-Lorentzian continuation, the authors show that boundary correlators admit two bulk descriptions: one integrating over the region outside the event horizon, and another integrating over the region between the event horizon and the inner Cauchy horizon. In the rotating case, a Poincaré-disc-like coordinate system adapted to the twist reveals that the same amplitudes can be represented either on the exterior region or on the Kruskal patch bounded by the Cauchy horizons, with an iε prescription consistent with the usual thermal behavior outside the horizon. The results reinforce the conjecture that holography encodes spacetime only up to the Cauchy horizon and thus implements strong cosmic censorship in AdS/CFT, while the Poincaré-disc analysis connects to prior insights about how the interior is captured by field theory degrees of freedom and boundary conditions. The work suggests future directions, including signs of Cauchy-horizon singular behavior in the CFT and extensions to higher dimensions.

Abstract

We investigate the description of the region behind the event horizon in rotating black holes in the AdS/CFT correspondence, using the rotating BTZ black hole as a concrete example. We extend a technique introduced by Kraus, Ooguri and Shenker [hep-th/0212277], based on analytically continuing amplitudes defined in a Euclidean space, to include rotation. In the rotating case, boundary amplitudes again have two different bulk descriptions, involving either integration only over the regions outside the black holes' event horizon, or integration over this region and the region between the event horizon and the Cauchy horizon (inner horizon). We argue that generally, the holographic map will relate the field theory to the region bounded by the Cauchy horizons in spacetime. We also argue that these results suggest that the holographic description of black holes will satisfy strong cosmic censorship.

Holography beyond the horizon and cosmic censorship

TL;DR

This work extends the Kraus-Ooguri-Shenker analytic-continuation program to rotating BTZ black holes in AdS/CFT, addressing how physics behind the event horizon is encoded in the boundary theory. Using bulk-boundary propagators built by the image method and a Euclidean-to-Lorentzian continuation, the authors show that boundary correlators admit two bulk descriptions: one integrating over the region outside the event horizon, and another integrating over the region between the event horizon and the inner Cauchy horizon. In the rotating case, a Poincaré-disc-like coordinate system adapted to the twist reveals that the same amplitudes can be represented either on the exterior region or on the Kruskal patch bounded by the Cauchy horizons, with an iε prescription consistent with the usual thermal behavior outside the horizon. The results reinforce the conjecture that holography encodes spacetime only up to the Cauchy horizon and thus implements strong cosmic censorship in AdS/CFT, while the Poincaré-disc analysis connects to prior insights about how the interior is captured by field theory degrees of freedom and boundary conditions. The work suggests future directions, including signs of Cauchy-horizon singular behavior in the CFT and extensions to higher dimensions.

Abstract

We investigate the description of the region behind the event horizon in rotating black holes in the AdS/CFT correspondence, using the rotating BTZ black hole as a concrete example. We extend a technique introduced by Kraus, Ooguri and Shenker [hep-th/0212277], based on analytically continuing amplitudes defined in a Euclidean space, to include rotation. In the rotating case, boundary amplitudes again have two different bulk descriptions, involving either integration only over the regions outside the black holes' event horizon, or integration over this region and the region between the event horizon and the Cauchy horizon (inner horizon). We argue that generally, the holographic map will relate the field theory to the region bounded by the Cauchy horizons in spacetime. We also argue that these results suggest that the holographic description of black holes will satisfy strong cosmic censorship.

Paper Structure

This paper contains 4 sections, 57 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Rotating BTZ black holes
  3. Poincare disc coordinates
  4. Conclusions

Figures (3)

  • Figure 1: Slices through AdS$_3$ in global coordinates, showing the regions of AdS$_3$ determined by the norm of the Killing vector $\xi =\partial_\phi$ in the coordinates (\ref{['rbtzb']}). In region 1, $\xi \cdot \xi \geq r_+^2$; in region 2, $r_+^2 \geq \xi \cdot \xi \geq r_-^2$; in region 3, $r_-^2 \geq \xi \cdot \xi > 0$; in region 4, $\xi \cdot \xi \leq 0$.
  • Figure 2: The analytic continuation and contour deformation in passing from the Euclidean to the Lorentzian section. The complex $z$ plane is pictured; on the right, translation invariance has been employed to move the original contour of integration to $z \in (-Z, -Z-2\pi i)$. To simplify the figure, only singularities associated with an external point in region $1_{++}$ have been indicated.
  • Figure 3: The analytic continuation and contour deformation in passing from the Euclidean to the Lorentzian section, in Poincare disc coordinates.