Abstract
We study the spontaneous scalarization of spherically symmetric, asymptoically flat boson stars in the (αℛ + γ mathcal{G} )ϕ2 scalar-tensor gravity model. These compact objects are made of a complex valued scalar field that has harmonic time dependence, while their space-time is static and they can reach densities and masses similar to that of supermassive black holes. We find that boson stars can be scalarized for both signs of the scalar-tensor coupling α and γ, respectively. This is, in particular, true for boson stars that are a priori stable with respect to decay into individual bosonic particles. A fundamental difference between the α- and γ-scalarization exists, though: while we find an interval in α > 0 for which boson stars can never be scalarized when γ = 0, there is no restriction on γ ≠ 0 when α = 0. Typically, two branches of solutions exist that differ in the way the boson star gets scalarized: either the scalar field is maximal at the center of the star, or on a shell with finite radius which roughly corresponds to the outer radius of the boson star. We also demonstrate that the former solutions can be radially excited.
Highlights
Q, where the latter can be interpreted as the number of scalar bosons of a given mass that form the boson star in a self-gravitating, bound system
We find that boson stars can be scalarized for both signs of the scalar-tensor coupling α and γ, respectively
Two branches of solutions exist that differ in the way the boson star gets scalarized: either the scalar field is maximal at the center of the star, or on a shell with finite radius which roughly corresponds to the outer radius of the boson star
Summary
The model we are studying here is a scalar-tensor gravity model that contains a nonminimal coupling between the square of a real scalar field and the Ricci scalar R as well as the Gauss-Bonnet term G: S=. In contrast to spherically symmetric, electro-vacuum black holes, boson stars have been shown to scalarize even when γ = 0 [44, 45] This is possible, because the energymomentum tensor of the Ψ-field has (in general) a non-vanishing trace T (Ψ) ≡ gμνTμ(Ψν ). In the perturbative limit (i.e. when neglecting backreaction of the scalar φ on the space-time), the Einstein equation tells us that R = −T (Ψ) and we would expect a tachyonic instability to be possible through scalar-tensor coupling of the αφ2R type Note that this is fundamentally different to the case of spherically symmetric, asymptotically flat electrovacuum black holes for which R = 0.
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