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Anisotropic flows into black holes. (English) Zbl 1540.83039

Summary: 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.

MSC:

83C57 Black holes
81T17 Renormalization group methods applied to problems in quantum field theory
83E05 Geometrodynamics and the holographic principle
83E30 String and superstring theories in gravitational theory

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