Boson stars with negative cosmological constant

TL;DR

This work analyzes boson star solutions in D-dimensional asymptotically anti-de Sitter spacetimes with a negative cosmological constant, detailing how Λ alters their mass, particle number, and asymptotic decay. By formulating the general framework, deriving a virial relation, and performing numerical studies in D=3,4,5, the authors show that Λ<0 generally lowers the maximal mass and preserves the qualitative structure seen in four-dimensional, Λ=0 cases for D>3, while D=3 exhibits distinct behavior. They establish a no-hair theorem for static AdS black holes with harmonic complex scalar fields, examine stability via linear perturbations, and compute the mass through AdS boundary counterterms, highlighting connections to the AdS/CFT correspondence. The results illuminate how spacetime dimensionality and AdS asymptotics influence solitonic gravitating scalar configurations and set the stage for further explorations in holography and higher-dimensional gravity.

Abstract

We consider boson star solutions in a $D$-dimensional, asymptotically anti-de Sitter spacetime and investigate the influence of the cosmological term on their properties. We find that for $D>4$ the boson star properties are close to those in four dimensions with a vanishing cosmological constant. A different behavior is noticed for the solutions in the three dimensional case. We establish also the non-existence of static, spherically symmetric black holes with a harmonically time-dependent complex scalar field in any dimension greater than two.