Abstract
The Schwarzschild singularity is known to be classically unstable. We demonstrate a simple holographic consequence of this fact, focusing on a perturbation that is uniform in boundary space and time. Deformation of the thermal state of the dual CFT by a relevant operator triggers a nonzero temperature holographic renormalization group flow in the bulk. This flow continues smoothly through the horizon and, at late interior time, deforms the Schwarzschild singularity into a more general Kasner universe. We show that the deformed near-singularity, trans-horizon Kasner exponents determine specific non-analytic corrections to the thermal correlation functions of heavy operators in the dual CFT, in the analytically continued ‘near-singularity’ regime.
Highlights
AdS black holes, and will couple gravity to a scalar field
We show that the deformed near-singularity, trans-horizon Kasner exponents determine specific non-analytic corrections to the thermal correlation functions of heavy operators in the dual CFT, in the analytically continued ‘near-singularity’ regime
We show that the Kasner exponent pt determines specific non-analytic corrections to the correlation function in the regime described by the bouncing geodesic
Summary
We can construct explicit examples of holographic flows from the AdS boundary to a Kasner singularity inside a black hole horizon. Integration from the boundary, through the horizon and to the singularity will determine the near-singularity behavior in terms of the ratio φo/T An example of such a solution is shown in figure 2. For every choice of the dimensionless CFT parameter φo/T , we obtain an emergent Kasner scaling determined by the exponent pt This relationship is shown in figure 3. A deformation of the exterior that preserves the spacetime symmetries of the thermal CFT state changes the near-singularity scaling exponents. This can be thought of as a dynamical instability of the Schwarzschild singularity at late interior time r. We describe how to extract these exponents using boundary probes
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