  Long-lived configurations of massive scalar fields around black holes may
form if the coupling between the mass of the scalar field and the mass of the
black hole is very small. In this work we analyze the effect of
self-interaction in the distribution of the long-lived cloud surrounding a
static black hole. We consider both attractive and repulsive self-interactions.
By solving numerically the Klein Gordon equation on a fixed background in the
frequency domain, we find that the spatial distribution of quasi stationary
states may be larger as compared to the non interacting case. We performed a
time evolution to determine the effect of the self-interaction on the life time
of the configurations our findings indicate that the contribution of the
self-interaction is subdominant.
