  We construct large classes of non-BPS smooth horizonless geometries that are
asymptotic to AdS$_3\times$S$^3\times$T$^4$ in type IIB supergravity. These
geometries are supported by electromagnetic flux corresponding to D1-D5
charges. We show that Einstein equations for systems with eight commuting
Killing vectors decompose into a set of Ernst equations, thereby admitting an
integrable structure. This feature, which can a priori be applied to other
AdS$_D\times\mathcal{C}$ settings in supergravity, allows us to use
solution-generating techniques associated with the Ernst formalism. We
explicitly derive solutions by applying the charged Weyl formalism that we have
previously developed. These are sourced internally by a chain of bolts that
correspond to regions where the orbits of the commuting Killing vectors
collapse smoothly. We show that these geometries can be interpreted as non-BPS
T$^4$ and S$^3$ deformations on global AdS$_3\times$S$^3\times$T$^4$ that are
located at the center of AdS$_3$. These non-BPS deformations can be made
arbitrarily small and should therefore correspond to non-supersymmetric
operators in the D1-D5 CFT. Finally, we also construct interesting bound states
of non-extremal BTZ black holes connected by regular bolts.
