Rotating Boson Stars Research Articles

Collapse and Nonlinear Instability of AdS Space with Angular Momentum.

We present a numerical study of rotational dynamics in AdS_{5} with equal angular momenta in the presence of a complex doublet scalar field. We determine that the endpoint of gravitational collapse is a Myers-Perry black hole for high energies and a hairy black hole for low energies. We investigate the time scale for collapse at low energies E, keeping the angular momenta J∝E in anti-de Sitter (AdS) length units. We find that the inclusion of angular momenta delays the collapse time, but retains a t∼1/E scaling. We perturb and evolve rotating boson stars, and find that boson stars near AdS space appear stable, but those sufficiently far from AdS space are unstable. We find that the dynamics of the boson star instability depend on the perturbation, resulting either in collapse to a Myers-Perry black hole, or development towards a stable oscillating solution.

On tidal disruption of clouds and disk formation near boson stars

We present two-dimensional general relativistic hydrodynamics simulations of free-falling gas clouds onto rotating boson stars (BS). Those objects consist of a complex scalar field coupled to gravity. BS are interesting as black hole (BH) mimickers. By this, one means that they are very compact objects but without any event horizon. It is then expected that the physics around BS is different than the one around BH. In this paper, we consider two BS configurations and study the trajectories and internal properties of infalling gas clouds, varying their initial positions. We follow the various disruption phases of the cloud until the formation, in some cases, of a gas torus in the inner region of the BS. We then discuss the cloud capture process by BS and the torus formation. We find that the characteristic time for torus formation increases when the initial distance between of the cloud and the BS decreases.

Light rings and light points of boson stars

This work is devoted to the study of photon trajectories around rotating boson stars. The basic properties of boson star models are given with a particular emphasis on the high compactness those objects can have. Using an effective potential method, circular orbits of photons around rotating boson stars are then obtained, at least for relativistic enough configurations. A particular class of light rings, in which the photons are at rest on a stable orbit, is exhibited. By this one means that the associated worldline is collinear to the Killing vector corresponding to the asymptotic time translation symmetry. It is proposed to call those orbits light points. Their existence is very specific to boson stars and the link between light points and ergoregions is investigated.

Analytical approximation for Newtonian boson stars in four and five dimensions

In this paper, we study rotating boson stars in the large coupling limit as well as in the Newtonian limit. We investigate the equilibrium solutions in four and five dimensions by adopting some analytical approximations. We show that the relations among the radius, angular momentum, Newtonian energy and quadrupole moment (for the four-dimensional solution) of the boson star can be qualitatively realized for the minimal number of boson star parameters.

Optical analogues of the Newton-Schrödinger equation and boson star evolution.

Many gravitational phenomena that lie at the core of our understanding of the Universe have not yet been directly observed. An example in this sense is the boson star that has been proposed as an alternative to some compact objects currently interpreted as being black holes. In the weak field limit, these stars are governed by the Newton–Schrodinger equation. Here we present an optical system that, under appropriate conditions, identically reproduces such equation in two dimensions. A rotating boson star is experimentally and numerically modelled by an optical beam propagating through a medium with a positive thermal nonlinearity and is shown to oscillate in time while also stable up to relatively high densities. For higher densities, instabilities lead to an apparent breakup of the star, yet coherence across the whole structure is maintained. These results show that optical analogues can be used to shed new light on inaccessible gravitational objects.

Chaotic lensing around boson stars and Kerr black holes with scalar hair

In a recent letter, arXiv:1509.00021, it was shown that the lensing of light around rotating boson stars and Kerr black holes with scalar hair can exhibit chaotic patterns. Since no separation of variables is known (or expected) for geodesic motion on these backgrounds, we examine the 2D effective potentials for photon trajectories, to obtain a deeper understanding of this phenomenon. We find that the emergence of stable light rings on the background spacetimes, allows the formation of "pockets" in one of the effective potentials, for open sets of impact parameters, leading to an effective trapping of some trajectories, dubbed quasi-bound orbits. We conclude that pocket formation induces chaotic scattering, although not all chaotic orbits are associated to pockets. These and other features are illustrated in a gallery of examples, obtained with a new ray-tracing code, PYHOLE, which includes tools for a simple, simultaneous visualization of the effective potential together with the spacetime trajectory, for any given point in a lensing image. An analysis of photon orbits allows us to further establish a positive correlation between photon orbits in chaotic regions and those with more than one turning point in the radial direction; we recall that the latter is not possible around Kerr black holes. Moreover, we observe that the existence of several light rings around a horizon (several fundamental orbits, including a stable one), is a central ingredient for the existence of multiple shadows of a single hairy black hole. We also exhibit the lensing and shadows by Kerr black holes with scalar hair, observed away from the equatorial plane, obtained with PYHOLE.

Astrophysical imaging of Kerr black holes with scalar hair

We address the astrophysical imaging of a family of deformed Kerr black holes (BHs). These are stationary, asymptotically flat black hole (BH) spacetimes, that are solutions of General Relativity minimally coupled to a massive, complex scalar field: Kerr BHs with scalar hair (KBHsSH). Such BHs bifurcate from the vacuum Kerr solution and can be regarded as a horizon within a rotating boson star. In a recent letter, it was shown that KBHsSH can exhibit very distinct shadows from the ones of their vacuum counterparts. The setup therein, however, considered the light source to be a celestial sphere sufficiently far away from the BH. Here, we analyse KBHsSH surrounded by an emitting torus of matter, simulating a more realistic astrophysical environment, and study the corresponding lensing of light as seen by a very far away observer, to appropriately model ground-based observations of Sgr A*. We find that the differences in imaging between KBHsSH and comparable vacuum Kerr BHs remain, albeit less dramatic than those observed for the corresponding shadows in the previous setup. In particular, we highlight two observables that might allow differentiating KBHsSH and Kerr BHs. The first is the angular size of the photon ring (in a Kerr spacetime) or lensing ring (in a KBHSH spacetime), the latter being significantly smaller for sufficiently non-Kerr-like spacetimes. The second is the existence of an edge in the intensity distribution (the photon ring in Kerr spacetime). This edge can disappear for very non-Kerr-like KBHsSH. It is plausible, therefore, that sufficiently precise Very Long Baseline Interferometric observations of BH candidates can constrain this model.

Iron Kα line of boson stars

The present paper is a sequel to our previous work [1] in which we studied the iron Kα line expected in the reflection spectrum of Kerr black holes with scalar hair. These metrics are solutions of Einstein's gravity minimally coupled to a massive, complex scalar field. They form a continuous bridge between a subset of Kerr black holes and a family of rotating boson stars depending on one extra parameter, the dimensionless scalar hair parameter q, ranging from 0 (Kerr black holes) to 1 (boson stars). Here we study the limiting case q = 1, corresponding to rotating boson stars. For comparison, spherical boson stars are also considered. We simulate observations with XIS/Suzaku. Using the fact that current observations are well fit by the Kerr solution and thus requiring that acceptable alternative compact objects must be compatible with a Kerr fit, we find that some boson star solutions are relatively easy to rule out as potential candidates to explain astrophysical black holes, while other solutions, which are neither too dilute nor too compact are more elusive and we argue that they cannot be distinguished from Kerr black holes by the analysis of the iron line with current X-ray facilities.

Kerr–Newman black holes with scalar hair

We construct electrically charged Kerr black holes (BHs) with scalar hair. Firstly, we take an uncharged scalar field, interacting with the electromagnetic field only indirectly, via the background metric. The corresponding family of solutions, dubbed Kerr-Newman BHs with ungauged scalar hair, reduces to (a sub-family of) Kerr-Newman BHs in the limit of vanishing scalar hair and to uncharged rotating boson stars in the limit of vanishing horizon. It adds one extra parameter to the uncharged solutions: the total electric charge. This leading electromagnetic multipole moment is unaffected by the scalar hair and can be computed by using Gauss's law on any closed 2-surface surrounding (a spatial section of) the event horizon. By contrast, the first sub-leading electromagnetic multipole -- the magnetic dipole moment --, gets suppressed by the scalar hair, such that the gyromagnetic ratio is always smaller than the Kerr-Newman value ($g=2$). Secondly, we consider a gauged scalar field and obtain a family of Kerr-Newman BHs with gauged scalar hair. The electrically charged scalar field now stores a part of the total electric charge, which can only be computed by applying Gauss' law at spatial infinity and introduces a new solitonic limit -- electrically charged rotating boson stars. In both cases, we analyse some physical properties of the solutions.

Iron Kα line of Kerr black holes with scalar hair

Recently, a family of hairy black holes in 4-dimensional Einstein gravity minimally coupled to a complex, massive scalar field was discovered [1]. Besides the mass M and spin angular momentum J, these objects are characterized by a Noether charge Q, measuring the amount of scalar hair, which is not associated to a Gauss law and cannot be measured at spatial infinity. Introducing a dimensionless scalar hair parameter q, ranging from 0 to 1, we recover (a subset of) Kerr black holes for q = 0 and a family of rotating boson stars for q = 1. In the present paper, we explore the possibility of measuring q for astrophysical black holes with current and future X-ray missions. We study the iron Kα line expected in the reflection spectrum of such hairy black holes and we simulate observations with Suzaku and eXTP. As a proof of concept, we point out, by analyzing a sample of hairy black holes, that current observations can already constrain the scalar hair parameter q, because black holes with q close to 1 would have iron lines definitively different from those we observe in the available data. We conclude that a detailed scanning of the full space of solutions, together with data from the future X-ray missions, like eXTP, will be able to put relevant constraints on the astrophysical realization of Kerr black holes with scalar hair.

Imaging a boson star at the Galactic center

Millimeter very long baseline interferometry will soon produce accurate images of the closest surroundings of the supermassive compact object at the center of the Galaxy, Sgr A*. These images may reveal the existence of a central faint region, the so-called shadow, which is often interpreted as the observable consequence of the event horizon of a black hole. In this paper, we compute images of an accretion torus around Sgr A* assuming this compact object is a boson star, i.e. an alternative to black holes within general relativity, with no event horizon and no hard surface. We show that very relativistic rotating boson stars produce images extremely similar to Kerr black holes, showing in particular shadow-like and photon-ring-like structures. This result highlights the extreme difficulty of unambiguously telling the existence of an event horizon from strong-field images.

Minimal boson stars in 5 dimensions: classical instability and existence of ergoregions

We show that minimal boson stars, i.e., boson stars that are made out of scalar fields without self-interaction, are always classically unstable in 5 spacetime dimensions. This is true for the non-rotating as well as rotating case with two equal angular momenta and in both Einstein and Gauss–Bonnet gravity, respectively, and contrasts with the 4-dimensional case, where classically stable minimal boson stars exist. We also discuss the appearance of ergoregions for rotating boson stars with two equal angular momenta. While rotating black holes typically possess an ergoregion, rotating compact objects without horizons such as boson stars have ergoregions only in a limited range of the parameter space. In this paper, we show for which values of the parameters these ergoregions appear and compare this with the case of standard Einstein gravity. We also point out that the interplay between Gauss–Bonnet gravity and rotation puts constraints on the behaviour of spacetime close to the rotation axis.

Circular geodesics and thick tori around rotating boson stars

Accretion disks play an important role in the evolution of their relativistic inner compact objects. The emergence of a new generation of interferometers will allow us to resolve these accretion disks and provide more information about the properties of the central gravitating object. Due to this instrumental leap forward it is crucial to investigate the accretion disk physics near various types of inner compact objects now to deduce later constraints on the central objects from observations. A possible candidate for the inner object is the boson star. Here, we will try to analyze the differences between accretion structures surrounding boson stars and black holes. We aim at analysing the physics of circular geodesics around boson stars and study simple thick accretion tori (so-called Polish doughnuts) in the vicinity of these stars. We realize a detailed study of the properties of circular geodesics around boson stars. We then perform a parameter study of thick tori with constant angular momentum surrounding boson stars. This is done using the boson star models computed by a code constructed with the spectral solver library KADATH. We demonstrate that all the circular stable orbits are bound. In the case of a constant angular momentum torus, a cusp in the torus surface exists only for boson stars with a strong gravitational scalar field. Moreover, for each inner radius of the disk, the allowed specific angular momentum values lie within a constrained range which depends on the boson star considered. We show that the accretion tori around boson stars have different characteristics than in the vicinity of a black hole. With future instruments it could be possible to use these differences to constrain the nature of compact objects.

Self-interacting boson stars with a single Killing vector field in anti–de Sitter space-time

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 vector 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.

Construction and physical properties of Kerr black holes with scalar hair

Kerr black holes (BHs) with scalar hair are solutions of the Einstein–Klein–Gordon field equations describing regular (on and outside an event horizon), asymptotically flat BHs with scalar hair (Herdeiro and Radu 2014 Phys. Rev. Lett. 112 221101). These BHs interpolate continuously between the Kerr solution and rotating boson stars in D = 4 spacetime dimensions. Here we provide details on their construction, discussing properties of the ansatz, the field equations, the boundary conditions and the numerical strategy. Then, we present an overview of the parameter space of the solutions, and describe in detail the space–time structure of the BH’s exterior geometry and of the scalar field for a sample of reference solutions. Phenomenological properties of potential astrophysical interest are also discussed, and the stability properties and possible generalizations are commented on. As supplementary material to this paper we make available numerical data files for the sample of reference solutions discussed, for public use (see stacks.iop.org/cqg/32/144001/mmedia).

Myers–Perry black holes with scalar hair and a mass gap: Unequal spins

We construct rotating boson stars and Myers–Perry black holes with scalar hair (MPBHsSH) as fully non-linear solutions of five dimensional Einstein gravity minimally coupled to a complex, massive scalar field. The MPBHsSH are, in general, regular on and outside the horizon, asymptotically flat, and possess angular momentum in a single rotation plane. They are supported by rotation and have no static limit. Such hairy BHs may be thought of as bound states of boson stars and singly spinning, vacuum MPBHs and inherit properties of both these building blocks. When the horizon area shrinks to zero, the solutions reduce to (in a single plane) rotating boson stars; but the extremal limit also yields a zero area horizon, as for singly spinning MPBHs. Similarly to the case of equal angular momenta, and in contrast to Kerr black holes with scalar hair, singly spinning MPBHsSH are disconnected from the vacuum black holes, due to a mass gap. We observe that for the general case, with two unequal angular momenta, the equilibrium condition for the existence of MPBHsSH is w=m1Ω1+m2Ω2, where Ωi are the horizon angular velocities in the two independent rotation planes and w,mi, i=1,2, are the scalar field's frequency and azimuthal harmonic indices.

Scalarized hairy black holes

In the presence of a complex scalar field scalar–tensor theory allows for scalarized rotating hairy black holes. We exhibit the domain of existence for these scalarized black holes, which is bounded by scalarized rotating boson stars and hairy black holes of General Relativity. We discuss the global properties of these solutions. Like their counterparts in general relativity, their angular momentum may exceed the Kerr bound, and their ergosurfaces may consist of a sphere and a ring, i.e., form an ergo-Saturn.

Models of rotating boson stars and geodesics around them: New type of orbits

We have developed a highly accurate numerical code capable of solving the coupled Einstein-Klein-Gordon system, in order to construct rotating boson stars in general relativity. Free fields and self-interacting fields, with quartic and sextic potentials, are considered. In particular, we present the first numerical solutions of rotating boson stars with rotational quantum number $k=3$ and $k=4$, as well as the first determination of the maximum mass of free-field boson stars with $k=2$. We have also investigated timelike geodesics in the spacetime generated by a rotating boson star for $k=1$, $2$ and $3$. A numerical integration of the geodesic equation has enabled us to identify a peculiar type of orbits: the zero-angular-momentum ones. These orbits pass very close to the center and are qualitatively different from orbits around a Kerr black hole. Should such orbits be observed, they would put stringent constraints on astrophysical compact objects like the Galactic center.

Black holes with only one Killing field

We present the first examples of black holes with only one Killing field. The solutions describe five dimensional AdS black holes with scalar hair. The black holes are neither stationary nor axisymmetric, but are invariant under a single Killing field which is tangent to the null generators of the horizon. Some of these solutions can be viewed as putting black holes into rotating boson stars. Others are related to the endpoint of a superradiant instability. For given mass and angular momentum (within a certain range) several black hole solutions exist.

Rotating boson stars in five dimensions

We study rotating boson stars in five spacetime dimensions. The boson fields consist of a complex doublet scalar field. Considering boson stars rotating in two orthogonal planes with both angular momenta of equal magnitude, a special ansatz for the boson field and the metric allows for solutions with nontrivial dependence on the radial coordinate only. The charge of the scalar field equals the sum of the angular momenta. The rotating boson stars are globally regular and asymptotically flat. For our choice of a sextic potential, the rotating boson star solutions possess a flat spacetime limit. We study the solutions in flat and curved spacetime.