Galileon accretion

We study steady-state spherically symmetric accretion of a Galileon field onto a Schwarzschild black hole in the test-fluid approximation. The Galileon is assumed to undergo a stage of cosmological evolution, thus setting a nontrivial boundary condition at spatial infinity. The critical flow is found for some parameters of the theory. There is a range of parameters when the critical flow exists, but the solution is unstable. It is also shown that for a certain range of parameters the critical flow solution does not exist. Depending on the model the sound horizon of the flow can be either outside or inside of the Schwarzschild horizon. The latter property may make it problematic to embed the Galileon theory in the standard black hole thermodynamics.