### Abstract

We explore physics behind the horizon in eternal AdS Schwarzschild black holes. In dimension d > 3, where the curvature grows large near the singularity, we find distinct but subtle signals of this singularity in the boundary CFT correlators. Building on previous work, we study correlation functions of operators on the two disjoint asymptotic boundaries of the spacetime by investigating the spacelike geodesies that join the boundaries. These dominate the correlators for large mass bulk fields. We show that the Penrose diagram for d > 3 is not square. As a result, the real geodesic connecting the two boundary points becomes almost null and bounces off the singularity at a finite boundary time t_{c} ≠ 0. If this geodesic were to dominate the correlator there would be a "light cone" singularity at t_{c}. However, general properties of the boundary theory rule this out. In fact, we argue that the correlator is actually dominated by a complexified geodesic, whose properties yield the large mass quasinormal mode frequencies previously found for this black hole. We find a branch cut in the correlator at small time (in the limit of large mass), arising from coincidence of three geodesics. The t_{c} singularity, a signal of the black hole singularity, occurs on a secondary sheet of the analytically continued correlator. Its properties are computationally accessible. The t_{c} singularity persists to all orders in the 1/m expansion, for finite α′, and to all orders in g_{s}. Certain leading nonperturbative effects can also be studied. The behavior of these boundary theory quantities near t_{c} gives, in principle, significant information about stringy and quantum behavior in the vicinity of the black hole singularity.

Original language | English (US) |
---|---|

Pages (from-to) | 365-409 |

Number of pages | 45 |

Journal | Journal of High Energy Physics |

Volume | 8 |

Issue number | 2 |

State | Published - Feb 1 2004 |

### Fingerprint

### Keywords

- AdS-CFT and dS-CFT Correspondence
- Black Holes
- Black Holes in String Theory

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*8*(2), 365-409.

**The black hole singularity in AdS/CFT.** / Fidkowski, Lukasz; Hubeny, Veronika; Kleban, Matthew; Shenker, Stephen.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 8, no. 2, pp. 365-409.

}

TY - JOUR

T1 - The black hole singularity in AdS/CFT

AU - Fidkowski, Lukasz

AU - Hubeny, Veronika

AU - Kleban, Matthew

AU - Shenker, Stephen

PY - 2004/2/1

Y1 - 2004/2/1

N2 - We explore physics behind the horizon in eternal AdS Schwarzschild black holes. In dimension d > 3, where the curvature grows large near the singularity, we find distinct but subtle signals of this singularity in the boundary CFT correlators. Building on previous work, we study correlation functions of operators on the two disjoint asymptotic boundaries of the spacetime by investigating the spacelike geodesies that join the boundaries. These dominate the correlators for large mass bulk fields. We show that the Penrose diagram for d > 3 is not square. As a result, the real geodesic connecting the two boundary points becomes almost null and bounces off the singularity at a finite boundary time tc ≠ 0. If this geodesic were to dominate the correlator there would be a "light cone" singularity at tc. However, general properties of the boundary theory rule this out. In fact, we argue that the correlator is actually dominated by a complexified geodesic, whose properties yield the large mass quasinormal mode frequencies previously found for this black hole. We find a branch cut in the correlator at small time (in the limit of large mass), arising from coincidence of three geodesics. The tc singularity, a signal of the black hole singularity, occurs on a secondary sheet of the analytically continued correlator. Its properties are computationally accessible. The tc singularity persists to all orders in the 1/m expansion, for finite α′, and to all orders in gs. Certain leading nonperturbative effects can also be studied. The behavior of these boundary theory quantities near tc gives, in principle, significant information about stringy and quantum behavior in the vicinity of the black hole singularity.

AB - We explore physics behind the horizon in eternal AdS Schwarzschild black holes. In dimension d > 3, where the curvature grows large near the singularity, we find distinct but subtle signals of this singularity in the boundary CFT correlators. Building on previous work, we study correlation functions of operators on the two disjoint asymptotic boundaries of the spacetime by investigating the spacelike geodesies that join the boundaries. These dominate the correlators for large mass bulk fields. We show that the Penrose diagram for d > 3 is not square. As a result, the real geodesic connecting the two boundary points becomes almost null and bounces off the singularity at a finite boundary time tc ≠ 0. If this geodesic were to dominate the correlator there would be a "light cone" singularity at tc. However, general properties of the boundary theory rule this out. In fact, we argue that the correlator is actually dominated by a complexified geodesic, whose properties yield the large mass quasinormal mode frequencies previously found for this black hole. We find a branch cut in the correlator at small time (in the limit of large mass), arising from coincidence of three geodesics. The tc singularity, a signal of the black hole singularity, occurs on a secondary sheet of the analytically continued correlator. Its properties are computationally accessible. The tc singularity persists to all orders in the 1/m expansion, for finite α′, and to all orders in gs. Certain leading nonperturbative effects can also be studied. The behavior of these boundary theory quantities near tc gives, in principle, significant information about stringy and quantum behavior in the vicinity of the black hole singularity.

KW - AdS-CFT and dS-CFT Correspondence

KW - Black Holes

KW - Black Holes in String Theory

UR - http://www.scopus.com/inward/record.url?scp=23044496353&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044496353&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:23044496353

VL - 8

SP - 365

EP - 409

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 2

ER -