  We investigate the accretion process for different spherically symmetric
space-time geometries for a static fluid. We analyse this procedure using the
most general black hole metric ansatz. After that, we examine the accretion
process for specific spherically symmetric metrics obtaining the velocity of
the sound during the process and the critical speed of the flow of the fluid
around the black hole. In addition, we study the behaviour of the rate of
change of the mass for each chosen metric for a barotropic fluid.
