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Physical Review D

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Cold planar horizons are floppy

Sean A. Hartnoll¹ and Jorge E. Santos^1,2

¹Department of Physics, Stanford University, Stanford, California 94305-4060, USA
²Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

Phys. Rev. D 89, 126002 – Published 3 June, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.126002

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 renormalization group 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.

Article Text

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