Three-charge superstrata with internal excitations

We construct a new family of three-charge $\frac{1}{8}-$BPS smooth solutions that have the same charges as the supersymmetric D1D5P Black Hole and are non-invariant under rotations of the compact manifold. We work in type IIB string theory on $T^4$ and we show how the supergravity and BPS equations reduce to a linear system, arranged in two `layers' of partial differential equations. We then build two solutions of our system of equations: the first is a superdescendant three-charge solution, obtained by acting with rigid symmetries on a seed two-charge solution, on which we can perform a non-trivial check for the system of equations; the second is a new superstratum solution that has both internal and external excitations. We then describe the CFT heavy states dual to these new geometries.