Spherical nonlinear absorption of cosmological scalar fields onto a black hole

In this paper we track the nonlinear spherical evolution of a massless scalar field onto a Schwarzschild black hole space-time as a first approximation to the accretion of cosmologically motivated classical scalar fields. We perform an analysis related to wave packets described by wave number and width. We study various values of the wave number k and find that for k = 0 and width packets bigger than the Schwarzschild radius, the absorption is not total. In the cases we study for k > 0, the black hole absorbs the total amount of energy density of the scalar field moving toward the horizon. Our results indicate that assuming spherical symmetry in the nonlinear regime, there are cases for which scalar fields are allowed to survive outside black holes and may eventually have lifetimes consistent with cosmological time scales.