Masking singularities with $k-$essence fields in an emergent gravity
  metric
  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 homogeneous field
configurations for the lagrangian $L=[{1\over
2}g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi]^{2}$ 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.
