The black hole singularity in AdS/CFT

By Lukasz Fidkowski, V. Hubeny, Matthew Kleban, S. Shenker. 2003

407 citations recorded by the source corpus.

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 geodesics 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c7bc3e2c511b3a6aed5317349d3972cd1dd8bca1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. D. Harlow
2. R. Myers
3. D. Stanford
4. V. Hubeny
5. L. Susskind
6. J. Maldacena
7. T. Takayanagi
8. Eric Perlmutter

In Nuclear and High Energy Physics

1. D. Harlow
2. R. Myers
3. D. Stanford
4. J. Maldacena
5. T. Takayanagi
6. Eric Perlmutter
7. L. Susskind
8. V. Hubeny

In Statistical and Nonlinear Physics

1. D. Harlow
2. R. Myers
3. D. Stanford
4. Thomas Hartman
5. Eric Perlmutter
6. L. Susskind
7. T. Takayanagi
8. V. Hubeny

Citations in the corpus

• A Holographic View on Physics out of Equilibrium (2010, background): “Indeed, it is precisely due to these regions that the CFT signals proposed in [191, 196] are present.”
• Inflation in AdS/CFT (2005, methodology): “In this case one can write down explicit formulas for boundary correlators that continue from AdS/CFT to dS/CFT.”
• Localized shocks (2014, methodology): “These include two-sided correlation functions [1, 2, 3], mutual information and entropy [4, 5, 6], and the pullbackpushforward [7, 8] modification of the standard smearing function procedure [9, 10, 11, 12].”
• Holographic entanglement entropy from 2d CFT: heavy states and local quenches (2014, methodology): “can be computed by geodesics in the WKB approximation (see for example [50]).”
• Holographic complexity in Vaidya spacetimes. Part II (2018, background): “We would like to understand this result in terms of boundary quantities and this is (15)Note that this corresponds to tL = tw and this simple result arises from the special property that the singularity is a straight horizontal line in a Penrose diagram describing the BTZ black hole [54].”
• Quantum computation vs. firewalls (2013, background): “Interesting previous work on the interior of AdS black holes includes [73, 74]; it would be illuminating to understand how to ask the firewall question in either of these frameworks.”
• Local Fluid Dynamical Entropy from Gravity (2008, unknown): “2.1 Coordinates adapted to a null geodesic congruence . . . . . . . . . . . . . . 8 2.2 Spacetime dual to hydrodynamics . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 The event horizon in the derivative expansion . . . . . . . . . . . . . . . .”
• Eikonal approximation in AdS/CFT: from shock waves to four-point functions (2006, unknown): “These results could then allow us to study, following reasonings along the lines of [19, 20, 21], the physics of the singularity in a full quantum gravity regime.”
• Krylov complexity in conformal field theory (2021, background): “[15] Lukasz Fidkowski, Veronika Hubeny, Matthew Kleban, and Stephen Shenker, “The black hole singularity in ads/cft,” Journal of High Energy Physics 2004, 014 (2004).”
• The AdS/CFT correspondence (2014, methodology): “38 Strictly speaking, if one fixes a conformal compactification so as to render the boundaries as straight vertical lines, one no longer has the freedom to keep the spacelike singularity drawn as a straight horizontal line [79]; instead the singularity bends inward.”
• Local bulk operators in AdS/CFT: A holographic description of the black hole interior (2006, methodology): “This shows quite explicitly that we can recover local physics outside the BTZ horizon using operators that act on a single copy of the CFT, while to describe the region inside the horizon we must use operators that act on both the CFT and its thermofield double [6, 16, 17, 18, 27].”
• Multiple shocks (2013, background): “In the bulk it is related to geodesics and hence probes the geometry [14, 15, 16, 17, 18, 19].”
• Holographic Duality with a View Toward Many-Body Physics (2009, background): “This relation between correlators of large ∆ observables and geodesics in the bulk theory offers a probe of the bulk spacetime [31, 32].”
• Black hole information, unitarity, and nonlocality (2006, background): “The problem of finding such geodesics was discussed for the similar problem of AdSSchwarzschild in [45].”
• Black holes in three dimensional higher spin gravity: a review (2012, background): “Two examples are the nature of entanglement of degrees of freedom inside and outside the horizon [11] and whether it is possible to access the region behind the black hole horizon by correlation functions of operators localized on the boundary [12,13].”
• Stringy effects in scrambling (2014, background): “In higher dimensions we expect interesting nonlinearities due to gravity, but the analysis in terms of geodesics is more complicated [67].”