Nonlinear evolution of unstable charged de Sitter black holes with hyperboloidal formalism
Abstract
We study the dynamical process of unstable charged de Sitter black holes. From the linear perturbation analysis, within certain range of the parameters, a charged scalar field can induce instability of the system. To reveal the real-time dynamics of such an instability, the nonlinear numerical simulation is implemented. The results show that the scalar field grows exponentially in the early stages and drastically extracts the charge from the black hole, analogous to the charged black hole in a closed system. Differently, after saturation, the scalar field can not coexist with the central black hole stably and dissipates beyond the cosmological horizon slowly, leaving behind a bald black hole. The static solutions, linear perturbations and dynamical evolutions are all done within the same, simple hyperboloidal framework.
