Boson stars with negative cosmological constant

TL;DR

This paper studies boson star solutions in higher-dimensional anti-de Sitter spacetimes, revealing dimension-dependent properties and proving the non-existence of certain black hole solutions with scalar fields.

Contribution

It extends the analysis of boson stars to D-dimensional AdS spaces and proves the non-existence of specific black hole solutions with scalar fields in higher dimensions.

Findings

Boson star properties in D>4 are similar to four-dimensional cases with zero cosmological constant.

Distinct behavior observed for boson stars in three dimensions.

Static, spherically symmetric black holes with time-dependent scalar fields do not exist in dimensions greater than two.

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.