Cold planar horizons are floppy

Understand

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.