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. Such oscillations 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.

What lies beyond the horizon of a holographic p-wave superconductor

“…The interior has subsequently been subjected to further study. This includes the introduction of additional field content and variation of coupling parameters [19][20][21][22][23], use of alternative black hole solutions [24][25][26], analysis of RG flows [27,28], as well as the construction of "no inner-horizon" theorems [29]. Interior solutions for the p-wave model are now also being investigated, with the analogous changes in geometry and matter fields being observed [30].…”