Cold planar horizons are floppy

Abstract

Extremal planar black holes of four dimensional Einstein-Maxwell theory with a negative cosmological constant have an AdS${}_2\times {\mathbb{R}}^2$ near horizon geometry. We show that this near horizon geometry admits a deformation to a two parameter family of extremal geometries with inhomogeneous, spatially periodic horizons. At a linear level, static inhomogeneous perturbations of AdS${}_2\times {\mathbb{R}}^2$ decay towards the horizon and thus appear irrelevant under the holographic RG flow. However we have found numerically that nonlinear effects lead to inhomogeneous near horizon geometries. A consequence of these observations is that an arbitrarily small periodic deformation of the boundary theory at nonzero charge density does not flow to AdS${}_2\times {\mathbb{R}}^2$ in the IR, but rather to an inhomogeneous horizon. These results shed light on existing numerical studies of low temperature periodically modulated black holes and also offer a new mechanism for holographic metal-insulator crossovers or transitions.

1+16 pages. 6 figures. v2 incorrect perturbative argument removed

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• Flux Compactifications Grow Lumps
• Generalized extremal branes in AdS/CMT and holographic superconductors
• The instability of $AdS$ black holes with lattices
• Disorder in AdS${}_3$/CFT${}_2$