Boson stars with negative cosmological constant

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.

Nonsingular spacetimes with a negative cosmological constant: Stationary solutions with matter fields

“…Recall that in [6] similar Einstein-scalar field solutions have been constructed with, however, V ≡ 0. Our condition V ′′ < 0 is evaded there by letting −ω 2 be an eigenvalue of the operator ψ → V D i (V D i ψ).…”

“…6) where the vanishing of the boundary term follows from elliptic regularity and density arguments. Thus Ω µ ≡ 0; equivalently, the L 2 kernel of g P is trivial.…”

“…All this leads naturally to the question of existence of stationary solutions of the Einstein equations with Λ < 0, with or without sources, and of properties thereof. Several families of such solutions have been recently constructed numerically [6,11,13,23,27,33,36]; cf. also [5] for a rigorous construction of static solutions of the Einstein-Vlasov equations with Λ < 0.…”

Black holes with scalar hair in Einstein–Gauss–Bonnet gravity

“…[13] for a review). Boson stars in d > 4 dimensional space-times were investigated namely in [14,15,16].…”

Hairy planar black holes in higher dimensions

“…However, in this case, since the solutions are domain walls, the singularity is not hidden by a horizon and the scalar flow is from φ = 0 at the boundary x = 1 to φ → ∞ at the singularity x = +∞. One resolution of this problem is to consider star solutions in AdS [43] which do not have a horizon and their entropy is much smaller than the black hole entropy (similar solutions with different scalar field configurations are the AdS boson stars [44,45]). …”