Dynamical spontaneous scalarization in Einstein-Maxwell-scalar models in anti-de Sitter spacetime

We study the dynamical spontaneous scalarization of charged black hole in asymptotically anti-de Sitter spacetimes in Einstein-Maxwell-scalar models. Including various nonminimal couplings between the scalar field and Maxwell field, an initial scalar-free black hole suffers tachyonic instability, and both the scalar field and the black hole irreducible mass grow exponentially at early times and saturate exponentially at late times. For fractional coupling, we find that, though there is negative energy distribution near the horizon, the black hole horizon area never decreases during the evolution. But when the parameters are large, the evolution end points of linearly unstable bald black holes will be spacetimes with a naked singularity such that the cosmic censorship is violated. The effects of the black hole charge, cosmological constant, and coupling strength on the dynamical scalarization process are studied in detail. We find that a large enough cosmological constant can prevent spontaneous scalarization.