Spontaneous scalarization of boson stars

Abstract

We study the spontaneous scalarization of spherically symmetric, asymptotically flat boson stars in the (αR+γG)φ 2 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. Introduction"Compact objects" is the name given to solutions in General Relativity (or alternative models of gravity) that are typically so dense that the curvature of space-time around them has detectable effects. A "measure" of the strength of the gravitational field of a body of mass M and radius R for r > R can be given by comparing the dimensionless ratio 2GM/(c 2 R) to unity, where G is Newton's constant and c the speed of light. For a white dwarf [1] and neutron star (for a recent review see e.g. [2]), this ratio is on the order of 2GM WD /(c 2 R WD ) ∼ O(10 −8 ) and 2GM NS /(c 2 R NS ) ∼ O(10 −1 ), respectively, but objects exist that are so dense, that R ≡ r h = c 2 /(2GM). These objects are called black holes [3], because the surface associated to r = r h is a surface of infinite redshift for an asymptotic observer, called event horizon. This means that any signal emitted from r ≤ r h cannot reach an asymptotic observer.While neutron stars have gravitational fields comparable to that of black holes, limits on their upper mass exist that are on the order of a few solar masses. Hence, they cannot account for the objects in the centre of galaxies that possess millions of solar masses in a spatially small region. It seems that the only viable and standard option are supermassive black holes [4] and this seems to have been confirmed by the recent observation of the center of M87 by the Event Horizon telescope [5]. An alternative, albeit more exotic, are compact objects made out of bosonic fields, the simplest example being the boson star made of a complex valued, massive scalar field [6][7][8][9][10][11][12]. The global U(1) symmetry in the model leads to a locally conserved Noether current and a globally conserved Noether charge Q, where the latter can be interpreted as the number of scalar bosons of a given mass that form the boson star in a selfgravitating, bound system. And, indeed, th...

Self-interacting multistate boson stars

“…the spontaneous scalarization of spherically symmetric, asymptotically flat boson stars in ref. [62]. Therefore, the second extension of our work is to study the spontaneous scalarization for axially symmetric BSs solutions.…”

Dynamic generation or removal of a scalar hair

“…The source terms in question could be a geometrically invariant quantity such as the Gauss-Bonnet invariant in extended Scalar-Gauss-Bonnet (sGB) theory [34][35][36][37][38][39][40][41][42], the Ricci scalar for non-conformally invariant black holes [43], the Chern-Simons invariant [44], and the Maxwell invariant F µν F µν [45]. More recently, further developments have been carried out on the spontaneous scalarization associated with compact objects [46][47][48][49][50][51][52][53] The presence of such non-minimal plays the role of an effective mass in the equation of motion of the scalar field, and the tachyonic instability might be triggered when the mass becomes negative.…”

Dynamic generation or removal of a scalar hair

“…The source terms in question could be a geometrically invariant quantity such as the Gauss-Bonnet invariant in extended Scalar-Gauss-Bonnet theory [34][35][36][37][38][39][40][41][42], the Ricci scalar for non-conformally invariant black holes [43], the Chern-Simons invariant [44], and the Maxwell invariant F µν F µν [45]. More recently, further developments have been carried out on the spontaneous scalarization associated with compact objects [46][47][48][49][50][51][52]. The presence of such non-minimal coupling plays the role of an effective mass in the equation of motion of the scalar field, and the tachyonic instability might be triggered when the mass becomes negative.…”