  We examine the stability of steady-state galileon accretion for the case of a
Schwarzshild black hole. Considering the galileon action up to the cubic term
in a static and spherically symmetric background we obtain the general solution
for the equation of motion which is divided in two branches. By perturbing this
solution we define an effective metric which determines the propagation of
fluctuations. In this general picture we establish the position of the sonic
horizon together with the matching condition of the two branches on it.
Restricting to the case of a Schwarzschild background, we show, via the
analysis of the energy of the perturbations and its time derivative, that the
accreting field is linearly stable.
