Late-time evolution of a charged massless scalar field in the spacetime of a dilaton black hole

We investigate the power-law tails. in the evolution of a charged massless scalar field around a fixed background of a dilaton black hole. Using both analytical and numerical methods we find the inverse power-law relaxation of charged fields at future timelike infinity, future null infinity, and along the outer horizon of the considered black hole. We envisage that a charged hair decays slower than neutral ones. The oscillatory inverse power law along the outer horizon of the dilaton black hole is of great importance for a mass inflation scenario along the Cauchy horizon of a dynamically formed dilaton black hole.