Scalar field instabilities in charged BTZ black holes

We investigate the charged scalar field propagating in a ($2+1$) charged Ba\~nados-Teitelboim-Zanelli black hole. The conditions for stability are studied unveiling, for each black hole geometry, the existence of a critical scalar charge as of the evolution is unstable. The existence of growing profiles is substantiated by the deep in the effective potential that intensifies as the scalar charge increases. The phenomenon happens in every black hole geometry even for small geometry charge. In the small scalar charge regime, the field evolution is stable and in such we calculate the quasinormal modes.