  Numerical simulations of the accretion of test scalar fields with
non-standard kinetic terms (of the k-essence type) onto a Schwarzschild black
hole are performed. We find a full dynamical solution for the spherical
accretion of a Dirac-Born-Infeld type scalar field. The simulations show that
the accretion eventually settles down to a well known stationary solution. This
particular analytical steady state solution maintains two separate horizons.
The standard horizon is for the usual particles propagating with the limiting
speed of light, while the other sonic horizon is for the k-essence
perturbations propagating with the speed of sound around this accreting
background. For the case where the k-essence perturbations propagate
superluminally, we show that one can send signals from within a black hole
during the approach to the stationary solution. We also find that a ghost
condensate model settles down to a stationary solution during the accretion
process.
