Late-time tails in gravitational collapse of a self-interacting (massive) scalar-field and decay of a self-interacting scalar hair

We study analytically the initial value problem for a self-interacting (massive) scalar field on a Reissner-Nordstr\"om spacetime. Following the no-hair theorem we examine the dynamical physical mechanism by which the self-interacting(SI) hair decays. We show analytically that the intermediate asymptotic behavior of SI perturbations is dominated by an oscillatory inverse power-law decaying tail. We confirm numerically this result. However, the numerical examination reveals that at late times the decay of SI hair is slower than any power law.