Anisotropic Flows into Black Holes

Abstract

We consider anisotropic black holes in the context of holographic renormalization group (RG) flows. We construct an $a$-function that is stationary at the boundary and the horizon and prove that it is also monotonic in both the exterior and the interior of the black hole. In spite of the reduced symmetry, we find that the "radial" null energy condition is sufficient to ensure the existence of this monotonic $a$-function. After constructing the $a$-function, we explore a holographic anisotropic $p$-wave superfluid state as a concrete example and numerical testing grounds. In doing so, we find that the $a$-function exhibits nontrivial oscillations in the trans-IR regime while preserving monotonicity. We find evidence that such oscillations appear to drive the trans-IR flow into nontrivial fixed points. We conclude by briefly discussing how our work fits into both the broader program of holographic RG flow and quantum information approaches to probing the black hole interior.

arXiv comment23 pages (including appendices) + references, 7 figures; v3: added appendix proving NEC in holographic p-wave superfluid + minor clarifications and corrections, version to appear in JHEP

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• Mixmasters in Wonderland: Chaotic dynamics from Carroll limits of gravity
• Diving inside holographic metals
• Holographic $a$-functions and Boomerang RG Flows
• Holographic Lifshitz flows
• Interior structure of the holographic s + p superconductor and chaotic-stable transition near the black hole singularity
• Flavors of entanglement