Dynamical charged black hole spontaneous scalarization in Anti-de Sitter\n spacetimes

Abstract

We study the fully nonlinear dynamics of black hole spontaneous\nscalarizations in Einstein-Maxwell scalar theory with coupling function\n$f(\\phi)=e^{-b\\phi^{2}}$, which can transform usual Reissner-Nordstr\\"om\nAnti-de Sitter (RN-AdS) black holes into hairy black holes. Fixing the\nArnowitt-Deser-Misner mass of the system, the initial scalar perturbation will\ndestroy the original RN-AdS black hole and turn it into a hairy black hole\nprovided that the constant $-b$ in the coupling function and the charge of the\noriginal black hole are sufficiently large, while the cosmological constant is\nsmall enough. In the scalarization process, we observe that the black hole\nirreducible mass initially increases exponentially, then it approaches to and\nfinally saturates at a finite value. Choosing stronger coupling and larger\nblack hole charge, we find that the black hole mass exponentially grows earlier\nand it takes a longer time for a hairy black hole to be developed and\nstabilized. We further examine phase structure properties in the scalarization\nprocess and confirm the observations in the non-linear dynamical study.\n