Scalar Field Dark Matter: behavior around black holes
  We present the numerical evolution of a massive test scalar fields around a
Schwarzschild space-time. We proceed by using hyperboloidal slices that
approach future null infinity, which is the boundary of scalar fields, and also
demand the slices to penetrate the event horizon of the black hole. This
approach allows the scalar field to be accreted by the black hole and to escape
toward future null infinity. We track the evolution of the energy density of
the scalar field, which determines the rate at which the scalar field is being
diluted. We find polynomial decay of the energy density of the scalar field,
and use it to estimate the rate of dilution of the field in time. Our findings
imply that the energy density of the scalar field decreases even five orders of
magnitude in time scales smaller than a year. This implies that if a
supermassive black hole is the Schwarzschild solution, then scalar field dark
matter would be diluted extremely fast
