In this paper we analyze Abelian-Higgs strings in a phenomenological model that takes quantum effects in curved space-time into account. This model, first introduced by Rastall, cannot be derived from an action principle. We formulate phenomenologica
l equations of motion under the guiding principle of minimal possible deformation of the standard equations. We construct string solutions that asymptote to a flat space-time with a deficit angle by solving the set of coupled non-linear ordinary differential equations numerically. Decreasing the Rastall parameter from its Einstein gravity value we find that the deficit angle of the space-time increases and becomes equal to $2pi$ at some critical value of this parameter that depends on the remaining couplings in the model. For smaller values the resulting solutions are supermassive string solutions possessing a singularity at a finite distance from the string core. Assuming the Higgs boson mass to be on the order of the gauge boson mass we find that also in Rastall gravity this happens only when the symmetry breaking scale is on the order of the Planck mass. We also observe that for specific values of the parameters in the model the energy per unit length becomes proportional to the winding number, i.e. the degree of the map $S^1 rightarrow S^1$. Unlike in the BPS limit in Einstein gravity, this is, however, not connect to an underlying mathematical structure, but rather constitutes a would-be-BPS bound.
We construct rotating boson stars in (4+1)-dimensional asymptotically Anti-de Sitter space-time (aAdS) with two equal angular momenta that are composed out of a massive and self-interacting scalar field. These solutions possess a single Killing vecto
r field. We construct explicit solutions of the equations in the case of a fixed AdS background and vanishing self-coupling of the scalar field. These are the generalizations of the oscillons discussed in the literature previously now taking the mass of the scalar field into account. We study the evolution of the spectrum of massive oscillons when taking backreaction and/or the self-coupling into account numerically. We observe that very compact boson stars possess an ergoregion.
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 t
o 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 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-reac
tion, 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.
The stability of black holes and solitons in d-dimensional Anti-de Sitter space-time against scalar field condensation is discussed. The resulting solutions are hairy black holes and solitons, respectively. In particular, we will discuss static black
hole solutions with hyperbolic, flat and spherical horizon topology and emphasize that two different type of instabilities exist depending on whether the scalar field is charged or uncharged, respectively. We will also discuss the influence of Gauss-Bonnet curvature terms. The results have applications within the AdS/CFT correspondence and describe e.g. holographic insulator/conductor/superconductor phase transitions.
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.
We study spherically symmetric soliton solutions in a model with a conformally coupled scalar field as well as in full conformal gravity. We observe that a new type of limiting behaviour appears for particular choices of the self-coupling of the scal
ar field, i.e. the solitons interpolate smoothly between the Anti-de Sitter vacuum and an uncharged configuration. Furthermore, within conformal gravity the qualitative approach of a limiting solution does not change when varying the charge of the scalar field - contrary to the Einstein-Hilbert case. However, it changes with the scalar self-coupling.
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 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 charge
d 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.
We study the stability of static as well as of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time which possess spherical horizon topology. We observe a non-linear instability related to the condensation of a charged, tac
hyonic scalar field and construct hairy black hole solutions of the full system of coupled Einstein, Maxwell and scalar field equations. We observe that the limiting solution for small horizon radius is either a hairy soliton solution or a singular solution that is not a regular extremal solution. Within the context of the gauge/gravity duality the condensation of the scalar field describes a holographic conductor/superconductor phase transition on the surface of a sphere.
