  It is known that dynamical solutions of the $k$-essence equation of motion
change the metric for the perturbations around these solutions and the
perturbations propagate in an emergent spacetime with metric $\tilde
G^{\mu\nu}$ different from the gravitational metric $g^{\mu\nu}$. We show that
for observers travelling with the perturbations, there exist field
configurations for the lagrangian $L=[{1\over
2}g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi]^{1\over 2}$ for which a
singularity in the gravitational metric $g^{\mu\nu}$ can be masked or hidden
for such observers. This is shown for the Schwarzschild and the
Reissner-Nordstrom metrics.
