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arXiv · 1403.4612

Cold planar horizons are floppy

Sean A. Hartnoll·Jorge E. Santos
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Abstract

Extremal planar black holes of four dimensional Einstein-Maxwell theory with a negative cosmological constant have an AdS$_2 \times \R^2$ 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$_2 \times \R^2$ 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$_2 \times \R^2$ 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.

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Sean A. Hartnoll, Jorge E. Santos. 2014-04-03. Cold planar horizons are floppy. https://doi.org/10.1103/physrevd.89.126002

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