Black hole interiors of homogeneous holographic solids under shear strain

Abstract: We investigate the interior of AdS black holes under finite shear strain in a class of holographic axion models, which are widely used to describe strongly-coupled systems with broken translations. We demonstrate that the shear anisotropy necessarily eliminates the inner Cauchy horizon, such that the deformed black hole approaches a space like singularity. The anisotropic effect induced by the axion fields triggers a collapse of the Einstein-Rosen bridge at the would-be Cauchy horizon, accompanied by a rapid change in the anisotropy of the spatial geometry. In addition, for a power-law axion potential, sufficiently large shear deformations give rise to a domain wall solution that includes a Lifshitz like scaling geometry near the boundary as well as a near horizon Kasner epoch with the Kasner exponents determined by the powers of the potential. Finally, we find that the interior dynamics of black holes generally enter an era described by an anisotropic Kasner universe at later interior time. Depending on the form of the potential, they either tend to stable Kasner universes, or exhibit an endless alternation of different Kasner epochs toward the singularity.