Striped phases from holography

We discuss new types of second order phase transitions in holography by constructing striped black holes in D=4 with $AdS_{4}$ asymptotics. In the context of $AdS/CFT$, they provide the gravity duals to field theory phases in which translational symmetry is spontaneously broken due to the formation of current density waves. These black holes are associated to three dimensional CFTs at finite temperature and deformed by a uniform chemical potential. We numerically solve a non-linear system of PDEs in order to construct the black hole geometries and extract some of their thermodynamic properties.