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We study the stability of charged solitons in 5-dimensional Anti-de Sitter (AdS) space-time. We show that for appropriate choices of the parameters of the model these solutions become unstable to form scalar hair. We find that the existence of charged solitons with scalar hair depends crucially on the charge and the mass of the scalar field. We investigate the dependence of the spectrum of solutions on the mass of the scalar field in detail. For positive mass of the scalar field the hairy solitons can be interpreted as charged boson stars. We find that for sufficiently small value of the charge of the scalar field a forbidden band of the boson star mass and charge exists, while all our results indicate that - contrary to the asymptotically flat space-time case - boson stars in asymptotically AdS can have arbitrarily large charge and mass.
We study the stability of static as well as of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time which possess spherical horizon topology. We observe a non-linear instability related to the condensation of a charged, tac
We obtain numerical solutions for rotating topological solitons of the nonlinear $sigma$-model in three-dimensional Anti-de Sitter space. Two types of solutions, $i)$ and $ii)$, are found. The $sigma$-model fields are everywhere well defined for both
We demonstrate that possession of a single negative mode is not a sufficient criterion for an instanton to mediate exponential decay. For example, de Sitter space is generically stable against decay via the Coleman-De Luccia instanton. This is due to
The stability of black holes and solitons in d-dimensional Anti-de Sitter space-time against scalar field condensation is discussed. The resulting solutions are hairy black holes and solitons, respectively. In particular, we will discuss static black
We study a two dimensional dilaton gravity system, recently examined by Almheiri and Polchinski, which describes near extremal black holes, or more generally, nearly $AdS_2$ spacetimes. The asymptotic symmetries of $AdS_2$ are all the time reparametr