Stability of charged solitons and formation of boson stars in five-dimensional anti-de Sitter spacetime

Abstract

We study the stability of charged solitons in 5-dimensional Anti-de Sitter (AdS) space-time. We show that for appropriate choices of the parameters of the model these solutions become unstable to form scalar hair. We find that the existence of charged solitons with scalar hair depends crucially on the charge and the mass of the scalar field. We investigate the dependence of the spectrum of solutions on the mass of the scalar field in detail. For positive mass of the scalar field the hairy solitons can be interpreted as charged boson stars. We find that for sufficiently small value of the charge of the scalar field a "forbidden band" of the boson star mass and charge exists, while all our results indicate that -contrary to the asymptotically flat space-time case -boson stars in asymptotically AdS can have arbitrarily large charge and mass.

Phases of global AdS black holes

“…When we add a scalar, in addition to global AdS and RN black hole, we have two new hairy saddle points of gravity: one is called the boson star (see eg., [14,15]) and the other is the hairy black hole. Depending on the boundary chemical potential and temperature, one of the four solutions dominates the free energy landscape, giving rise to an intricate phase diagram.…”

“…we will have ψ (1) = 0 (scalar condensate), without the formation of a horizon. This configuration is called Boson star [14]. Here, boundary conditions at r = 0 is given by φ (0) = 0, h (0) = 0, ψ (0) = 0, g (0) = 0 which ensure that there is no kink at r = 0.…”

Charged compact boson stars and shells in the presence of a cosmological constant

“…Boson stars and boson shells representing the localized self-gravitating solutions were introduced long ago [1-3] and they have been studied vary widely in the literature . Such theories are being considered in the presence of positive [14][15][16][17] as well as negative [15,[17][18][19][20][21] values of the cosmological constant Λ. The theories with positive values of Λ (corresponding to the de Sitter (dS) space) are relevant from observational point of view as they describe a more realistic description of the compact stars in the universe since all the observations seem to indicate the existence of a positive cosmological constant.…”

Boson stars in a theory of complex scalar field coupled to gravity

“…We have studied the properties of these solutions and have also determined their domains of existence for some specific values of the parameters of the theory. Similar solutions have also been obtained by Hartmann, Kleihaus, Kunz, and Schaffer, in a V-shaped scalar potential.A study of boson shells and boson stars in scalar electrodynamics with a self-interacting complex scalar field Φ coupled to Einstein gravity is of a very wide interest in the gravity theories[1]- [26] . Hartmann, Kleihaus, Kunz, and Schaffer (HKKS) [2,3] have recently studied boson stars in a theory of complex scalar field coupled to Einstein gravity in a V-shaped scalar potential: V (ΦΦ * ) ≡ V (|Φ|) = λ c |Φ| (where λ c is a constant).…”