Cloud Screening of Extremal Charged BTZ Black Hole

This paper investigates the dynamics of a charged scalar field near the horizon of an extremal charged BTZ black hole. It demonstrates that the electric field in the near-horizon AdS2 region can trigger an instability, which is resolved by the formation of a scalar cloud. This cloud screens the electric flux, leading to a self-consistent stationary configuration. The paper provides an analytical solution for the scalar profile and discusses its implications, offering insights into electric screening in black holes and the role of near-horizon dynamics.