Dynamical formation of axionic hair around a charged black hole

In this paper, we present a nonlinear numerical investigation on the dynamical scalarization process of a Reissner-Nordstr"om black hole, incorporating an axionic scalar potential within the framework of the Einstein-Maxwell-dilaton theory. By scrutinizing the evolution of the irreducible mass of the black hole and the value of the scalar field on the apparent horizon across various parameters of the axionic potential, we elucidate the correlations between the final states of scalarized charged black hole and the axionic potential. We observe that the inclusion of the axionic potential can either decrease or increase the irreducible mass of the final scalarized black hole, depending on the strength of the coupling between the dilaton and the electric invariant ${F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}$. Regarding the value of the scalar field on the apparent horizon, we find that it decreases with the inclusion of the axionic potential. Our results contribute to an important understanding of the dynamical scalarization of black holes and the potential configurations of scalar hair with various self-interactions.