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We present compact Q-balls in an (Anti-)de Sitter background in D dimensions, obtained with a V-shaped potential of the scalar field. Beyond critical values of the cosmological constant compact Q-shells arise. By including the gravitational back-reaction, we obtain boson stars and boson shells with (Anti-)de Sitter asymptotics. We analyze the physical properties of these solutions and determine their domain of existence. In four dimensions we address some astrophysical aspects.
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We study the spontaneous scalarization of spherically symmetric, asymptotically flat boson stars in the $(alpha {cal R} + gamma {cal G}) phi^2$ 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 $alpha$ and $gamma$, respectively. This is, in particular, true for boson stars that are {it a priori} stable with respect to decay into individual bosonic particles. A fundamental difference between the $alpha$- and $gamma$-scalarization exists, though: while we find an interval in $alpha > 0$ for which boson stars can {it never} be scalarized when $gamma=0$, there is no restriction on $gamma eq 0$ when $alpha=0$. 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.
For a theory in which a scalar field $phi$ has a nonminimal derivative coupling to the Einstein tensor $G_{mu u}$ of the form $phi,G_{mu u} abla^{mu} abla^{ u} phi$, it is known that there exists a branch of static and spherically-symmetric relativistic stars endowed with a scalar hair in their interiors. We study the stability of such hairy solutions with a radial field dependence $phi(r)$ against odd- and even-parity perturbations. We show that, for the star compactness ${cal C}$ smaller than $1/3$, they are prone to Laplacian instabilities of the even-parity perturbation associated with the scalar-field propagation along an angular direction. Even for ${cal C}>1/3$, the hairy star solutions are subject to ghost instabilities. We also find that even the other branch with a vanishing background field derivative is unstable for a positive perfect-fluid pressure, due to nonstandard propagation of the field perturbation $delta phi$ inside the star. Thus, there are no stable star configurations in derivative coupling theory without a standard kinetic term, including both relativistic and nonrelativistic compact objects.
We construct electrically charged Q-balls and boson stars in a model with a scalar self-interaction potential resulting from gauge mediated supersymmetry breaking. We discuss the properties of these solutions in detail and emphasize the differences to the uncharged case. We observe that Q-balls can only be constructed up to a maximal value of the charge of the scalar field, while for boson stars the interplay between the attractive gravitational force and the repulsive electromagnetic force determines their behaviour. We find that the vacuum is stable with respect to pair production in the presence of our charged boson stars. We also study the motion of charged, massive test particles in the space-time of boson stars. We find that in contrast to charged black holes the motion of charged test particles in charged boson star space-times is planar, but that the presence of the scalar field plays a crucial role for the qualitative features of the trajectories. Applications of this test particle motion can be made in the study of extreme-mass ratio inspirals (EMRIs) as well as astrophysical plasmas relevant e.g. in the formation of accretion discs and polar jets of compact objects.
We study the geodesic motion of test particles in the space-time of non-compact boson stars. These objects are made of a self-interacting scalar field and -- depending on the scalar fields mass -- can be as dense as neutron stars or even black holes. In contrast to the former these objects do not contain a well-defined surface, while in contrast to the latter the space-time of boson stars is globally regular, can -- however -- only be given numerically. Hence, the geodesic equation also has to be studied numerically. We discuss the possible orbits for massive and massless test particles and classify them according to the particles energy and angular momentum. The space-time of a boson star approaches the Schwarzschild space-time asymptotically, however deviates strongly from it close to the center of the star. As a consequence, we find additional bound orbits of massive test particles close to the center of the star that are not present in the Schwarzschild case. Our results can be used to make predictions about extreme-mass-ratio inspirals (EMRIs) and we hence compare our results to recent observational data of the stars orbiting Sagittarius A* - the radiosource at the center of our own galaxy.
We construct boson stars in (4+1)-dimensional Gauss-Bonnet gravity. We study the properties of the solutions in dependence on the coupling constants and investigate these in detail. While the thick wall limit is independent of the value of the Gauss-Bonnet coupling, we find that the spiraling behaviour characteristic for boson stars in standard Einstein gravity disappears for large enough values of the Gauss-Bonnet coupling. Our results show that in this case the scalar field can not have arbitrarily high values at the center of the boson star and that it is hence impossible to reach the thin wall limit. Moreover, for large enough Gauss-Bonnet coupling we find a unique relation between the mass and the radius (qualitatively similar to those of neutron stars) which is not present in the Einstein gravity limit.
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