  In holographic applications one can encounter scenarios where a
long-wavelength instability can arise. In such situations, it is often the case
that the dynamical end point of the instability is a new equilibrium phase with
a nonlinear scalar hair condensate outside the black hole horizon. We here
review holographic setups where symmetric horizons suffer from long-wavelength
instabilities where a suitable equilibrium condensate phase does not exist. We
study the dynamics of the simplest model in this exotic class, and show that it
uncovers arbitrarily large curvatures in the vicinity of the horizon which
asymptotically turn such region singular, at finite time with respect to the
boundary theory.
