Classical scalar fields have been proposed as possible candidates for the
dark matter component of the universe. Given the fact that super-massive black
holes seem to exist at the center of most galaxies, in order to be a viable
candidate for the dark matter halo a scalar field configuration should be
stable in the presence of a central black hole, or at least be able to survive
for cosmological time-scales. In the present work we consider a scalar field as
a test field on a Schwarzschild background, and study under which conditions
one can obtain long-lived configurations. We present a detailed study of the
Klein-Gordon equation in the Schwarzschild spacetime, both from an analytical
and numerical point of view, and show that indeed there exist quasi-stationary
solutions that can remain surrounding a black hole for large time-scales.Comment: 34 pages, 13 figure