Charged and radially excited boson stars (in Anti-de Sitter)

We study charged and radially excited boson stars in both asymptotically flat as well as asymptotically Anti-de Sitter space-time. We demonstrate that two different types of radially excited solutions exist~: one that persists in the linear limit of small scalar fields, in which analytical arguments suggest the existence of these solutions, and one that appears only in the highly non-linear regime of the model. We also demonstrate that the formation of wavy scalar hair discussed previously for black holes and boson stars in asymptotically flat space-time persists for asymptotically Anti-de Sitter space-time