Rotating Boson Stars Research Articles

Comparison of magnetized thick disks around black holes and boson stars

Boson stars are considered as promising candidates for black hole mimickers. Similar to other compact objects they can form accretion disks around them. The properties of these disks could possibly distinguish them from other compact objects like black holes in future observations. Retrograde thick disks around boson stars and the influence of strong magnetic fields on them were already studied and it was shown that they can harbor very distinct features compared to black hole disks. However, the case of prograde thick disks is mostly unexplored, since they may appear much more similar to black hole disks. In this work we will investigate similarities and differences regarding prograde thick disks around non-selfinteracting rotating boson stars and rotating black holes. We assume thereby a polytropic equation of state and a constant specific angular momentum distribution of the disks. We classify the various conceivable boson star and black hole solutions by a dimensionless spin parameter a and compare their corresponding disk solutions. The influence of toroidal magnetic fields on the disks is analyzed by selected disk properties, as the rest-mass density distribution and the Bernoulli parameter. Disk solutions are characterized by their degree of magnetization represented by the magnetization parameter βmc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _{mc}$$\\end{document}. We found that strong magnetic fields can strengthen the differences of disk solutions or oppositely even lead to a correlation in disk properties, depending on the spin parameter of the boson star and black hole solutions. We identify the vertical thickness of the boson star disks as the main differentiating factor, since for most solutions the vertical density distribution is far more outreaching for boson star disks compared to black hole disks.

Extreme-mass-ratio inspirals into rotating boson stars: Nonintegrability, chaos, and transient resonances

Extreme-mass-ratio inspirals into rotating boson stars: Nonintegrability, chaos, and transient resonances

Charged and rotating boson stars in five-dimensional Einstein-Maxwell-Chern-Simons theory

Charged and rotating boson stars in five-dimensional Einstein-Maxwell-Chern-Simons theory

Binary boson stars: Merger dynamics and formation of rotating remnant stars

Scalar boson stars have attracted attention as simple models for exploring the nonlinear dynamics of a large class of ultra compact and black hole mimicking objects. Here, we study the impact of interactions in the scalar matter making up these stars. In particular, we show the pivotal role the scalar phase and vortex structure play during the late inspiral, merger, and post-merger oscillations of a binary boson star, as well as their impact on the properties of the merger remnant. To that end, we construct constraint satisfying binary boson star initial data and numerically evolve the nonlinear set of Einstein-Klein-Gordon equations. We demonstrate that the scalar interactions can significantly affect the inspiral gravitational wave amplitude and phase, and the length of a potential hypermassive phase shortly after merger. If a black hole is formed after merger, we find its spin angular momentum to be consistent with similar binary black hole and binary neutron star merger remnants. Furthermore, we formulate a mapping that approximately predicts the remnant properties of any given binary boson star merger. Guided by this mapping, we use numerical evolutions to explicitly demonstrate, for the first time, that rotating boson stars can form as remnants from the merger of two non-spinning boson stars. We characterize this new formation mechanism and discuss its robustness. Finally, we comment on the implications for rotating Proca stars.

Magnetized thick disks around boson stars

The effects of magnetic fields on accretion disks around compact objects are of high importance in the study of their general properties and dynamics. Here we analyze the influence of magnetic fields on thick accretion disks around rotating boson stars. We assume a uniform constant specific angular momentum distribution and a polytropic equation of state. The purely hydrodynamical thick disk solutions are extended to magnetized solutions by adding a toroidal magnetic field and then analyzed in terms of a magnetization parameter. We consider one-centered solutions as well as two-centered solutions and focus on retrograde tori, since they are more distinctive due to their unique properties. Our computed solutions indicate that strong magnetic fields influence the characteristics of thick disks around rotating boson stars and possibly affect their unique features.

Universal relations for rotating boson stars

Boson stars represent a hypothetical exotic type of compact stellar object that may be observed from the gravitational signal of coalescing binaries in current and future gravitational wave (GW) detectors. In this work we show that the moment of inertia $I$, the (dimensionless) angular momentum $\ensuremath{\chi}$, and the quadrupole moment $Q$ of rotating boson stars obey a universal relation, valid for a wide set of boson star models. Further, the obtained $I\ensuremath{-}\ensuremath{\chi}\ensuremath{-}Q$ relation clearly differs from its famous neutron star counterpart, providing us with an unequivocal diagnostic tool to distinguish boson stars from ordinary compact stars or other celestial bodies in GW observations. Such universal (i.e., model-independent) relations also provide a useful tool to probe the strong gravity regime of general relativity and to constrain the equation of state of matter inside compact stars.

Equatorial orbits of spinning test particles in rotating boson stars

In this paper, we study circular orbits of spinning test particles in the background of a rotating boson star. Using the pole-dipole approximation and neglecting the back-reaction of the spinning test particle on the spacetime, the equation of motion of the spinning test particle is described by the Mathisson–Papapetrou–Dixon equation. We solve this equation under the Tulczyjew spin-supplementary condition and obtain the four-momentum and four-velocity of the spinning test particle. Quite different from the spinless particle, the effective potential of the spinning particle with zero orbital angular momentum goes to infinite at the center of the rotating boson star. This will lead to the fact that the spinning particle can not pass through the center of the boson star. However, when the spin angular momentum and orbital angular momentum satisfy 2{bar{s}}+{bar{l}}=0, the effective potential is not divergent anymore and the spinning particle can pass through the center of the rotating boson star. We still investigate how the spin affects the structure of the circular orbits and we find that the spin will induce the larger or smaller regions of no circular orbits, unstable circular orbits, and stable circular orbits. Moreover, the radius and energy of the circular orbit will be decreased or increased by the particle spin. These results will have an important application in testing the gravitational waves in the boson star background.

Chains of rotating boson stars

Boson stars are stationary, axially symmetric solutions of a complex scalar field theory coupled to gravity. Recently, multisolitonic configurations interpreted as static chains of multiple boson stars bound by gravity and carrying no angular momentum were reported. We propose to generalize those solutions to the stationary case by constructing chains of rotating boson stars and analyze their properties. The nonlinear elliptic field equations are solved using the finite element method. We find that chains with an even number of constituents exhibit the same spiral-like frequency dependence of their mass, angular momentum and Noether charge as single boson stars. In contrast, sequences of chains with an odd number of constituents show nontrivial loops starting and ending at the flat vacuum. As a consequence, such solutions cannot be uniquely parametrized by a single parameter. We conjecture that all rotating chains correspond to excitations of single boson stars or pairs of them. We also analyze their flat space limit and find that they reduce to chains of $Q$-balls.

Motion of test particle in rotating boson star

Motion of a test particle plays an important role in understanding the properties of a spacetime. As a new type of the strong gravity system, boson stars could mimic black holes located at the center of galaxies. Studying the motion of a test particle in the spacetime of a rotating boson star will provide the astrophysical observable effects if a boson star is located at the center of a galaxy. In this paper, we investigate the timelike geodesic of a test particle in the background of a rotating boson star with angular number $m=(1, 2, 3)$. With the change of angular number and frequency, a rotating boson star will transform from the low rotating state to the highly relativistic rapidly rotating state, the corresponding Lense-Thirring effects will be more and more significant and it should be studied in detail. By solving the four-velocity of a test particle and integrating the geodesics, we investigate the bound orbits with a zero and nonzero angular momentum. We find that a test particle can stay more longer time in the central region of a boson star when the boson star becomes from low rotating state to highly relativistic rotating state. Comparing the periapse values of the orbits obtained in rotating boson stars and the corresponding orbits of the observed stars orbiting Sagittarius $A^*$, we discuss the possible observable effects of the astrophysical boson star in the Galactic center.

Thick toroidal configurations around scalarized Kerr black holes

In this work we aim to investigate thick tori configurations around Kerr black holes with scalar hair (KBHsSH). For that goal, we provide a first approach using constant specific angular momentum non-self-gravitating Polish doughnuts. Through a series of examples, we show the feasibility of new topologies, such as double-centered tori with two cusps as well as similar structures as the ones found for rotating boson stars (BSs), namely, tori endowed with two centers and a single cusp. These KBHsSH solutions are also shown to possibly house static surfaces, associated with the static rings present in these spacetimes. Through this paper we highlight the differences between these fluid configurations when housed by some KBHsSH examples, standard Kerr black holes and rotating BSs.

Rotating boson stars using finite differences and global Newton methods

We study rotating boson star data for numerical relativity using a 3 + 1 decomposition adapted to a curvilinear axisymmetric spacetime with regularization at the rotation axis. The Einstein–Klein–Gordon equations result in a system of six coupled, elliptic, nonlinear equations with an added unknown for the scalar field’s frequency ω. Utilizing a Cartesian two-dimensional grid, fourth-order finite differences, and global Newton methods, we generated seven data sets characterized by a rotation azimuthal integer l ∈ [0, 6]. Our numerical implementation is shown to correctly converge both with respect to the resolution size and boundary extension. Thus, global parameters such as the Komar masses and angular momenta can be precisely calculated to characterize these spacetimes. Furthermore, analyzing each family at fixed rotation integer l produces maximum masses and minimum rotation frequencies. Our results coincide with previous results in literature for l ∈ [0, 2] [as in references (Yoshida and Eriguchi 1997 Phys. Rev. D 56 6370; Lai 2004 PhD Thesis; Grandclément, et al 2014 Phys. Rev. D 90 024068; Liebling and Palenzuela 2017 Living Rev. Relativ. 20)], and are new for l > 2. In particular, the study of high-amplitude and localized scalar fields in axial symmetry is revealed to be only possible by adding the sixth regularization variable, thus reaffirming previous work on the importance of regularization in curvilinear-based numerical relativity. These results also provide the groundwork for extending this research to other self-gravitating systems, such as rotating boson stars with nonlinear self-interactions, or the case of massive vector fields.

New solutions for rotating boson stars

It has been shown that scalar fields can form gravitationally bound compact objects called boson stars. In this study, we analyze boson star configurations where the scalar fields contain a small amount of angular momentum and find two new classes of solutions. In the first case all particles are in the same slowly rotating state, and in the second case the majority of particles are in the nonrotating ground state and a small number of particles are in an excited rotating state. In both cases, we solve the underlying Gross-Pitaevskii-Poisson equations that describe the profile of these compact objects both numerically as well as analytically through series expansions.

Retrograde polish doughnuts around boson stars

We investigate polish doughnuts with a uniform constant specific angular momentum distribution in the space-times of rotating boson stars. In such space-times thick tori can exhibit unique features not present in Kerr space-times. For instance, in the context of retrograde tori, they may possess two centers connected or not by a cusp. Rotating boson stars also feature a static ring, neither present in Kerr space-times. This static ring consists of static orbits, where particles are at rest with respect to a zero angular momentum observer at infinity. Here we show that the presence of a static ring allows for an associated static surface of a retrograde thick torus, where inside the static surface the fluid moves in prograde direction. We classify the retrograde Polish doughnuts and present several specific examples.

Stability of rotating scalar boson stars with nonlinear interactions

We study the stability of rotating scalar boson stars, comparing those made from a simple massive complex scalar (referred to as mini boson stars), to those with several different types of nonlinear interactions. To that end, we numerically evolve the nonlinear Einstein-Klein-Gordon equations in 3D, beginning with stationary boson star solutions. We show that the linear, non-axisymmetric instability found in mini boson stars with azimuthal number $m=1$ persists across the entire parameter space for these stars, though the timescale diverges in the Newtonian limit. Therefore, any boson star with $m=1$ that is sufficiently far into the non-relativistic regime, where the leading order mass term dominates, will be unstable, independent of the nonlinear scalar self-interactions. However, we do find regions of $m=1$ boson star parameter space where adding nonlinear interactions to the scalar potential quenches the non-axisymmetric instability, both on the non-relativistic, and the relativistic branches of solutions. We also consider select boson stars with $m=2$, finding instability in all cases. For the cases exhibiting instability, we follow the nonlinear development, finding a range of dynamics including fragmentation into multiple unbound non-rotating stars, and formation of binary black holes. Finally, we comment on the relationship between stability and criteria based on the rotating boson star's frequency in relation to that of a spherical boson star or the existence of a co-rotation point. The boson stars that we find not to exhibit instability when evolved for many dynamical times include rapidly rotating cases where the compactness is comparable to that of a black hole or neutron star.

Geometric modeling of M87* as a Kerr black hole or a non-Kerr compact object

Context. The Event Horizon Telescope (EHT) collaboration recently obtained the first images of the surroundings of the supermassive compact object M87* at the center of the galaxy M87. This provides a fascinating probe of the properties of matter and radiation in strong gravitational fields. It is important to determine from the analysis of these results what can and cannot be inferred about the nature of spacetime around M87* Aims. We want to develop a simple analytic disk model for the accretion flow of M87*. Compared to general-relativistic magnetohydrodynamic models, this new approach has the advantage that it is independent of the turbulent character of the flow and is controlled by only a few easy-to-interpret, physically meaningful parameters. We want to use this model to predict the image of M87*, assuming that it is either a Kerr black hole or an alternative compact object. Methods. We computed the synchrotron emission from the disk model and propagate the resulting light rays to the far-away observer by means of relativistic ray tracing. Such computations were performed assuming different spacetimes, such as Kerr, Minkowski, nonrotating ultracompact star, rotating boson star, or Lamy spinning wormhole. We performed numerical fits of these models to the EHT data. Results. We discuss the highly lensed features of Kerr images and show that they are intrinsically linked to the accretion-flow properties and not only to gravitation. This fact is illustrated by the notion of the secondary ring, which we introduce. Our model of a spinning Kerr black hole predicts mass and orientation consistent with the EHT interpretation. The non-Kerr images result in a similar quality of numerical fits and may appear very similar to Kerr images, once blurred to the EHT resolution. This implies that a strong test of the Kerr spacetime may be out of reach with the current data. We note that future developments of the EHT could alter this situation. Conclusions. Our results show the importance of studying alternatives to the Kerr spacetime to be able to test the Kerr paradigm unambiguously. More sophisticated treatments of non-Kerr spacetimes and more advanced observations are needed to proceed further in this direction.

Rotating multistate boson stars

In this paper, we construct rotating boson stars composed of the coexisting states of two scalar fields, including the ground and first excited states. We show the coexisting phase with both the ground and first excited states for rotating multistate boson stars. In contrast to the solutions of the nodeless boson stars, the rotating boson stars with two states have two types of nodes, including the $^1S^2S$ state and the $^1S^2P$ state. Moreover, we explore the properties of the mass $M$ of rotating boson stars with two states as a function of the synchronized frequency $\omega$, as well as the nonsynchronized frequency $\omega_2$. Finally, we also study the dependence of the mass $M$ of rotating boson stars with two states on angular momentum for both the synchronized frequency $\omega$ and the nonsynchronized frequency $\omega_2$.

Kerr black holes with synchronised scalar hair and boson stars in the Einstein-Friedberg-Lee-Sirlin model

We consider the Friedberg-Lee-Sirlin model minimally coupled to Einstein gravity in four spacetime dimensions. The renormalizable Friedberg-Lee-Sirlin model consists of two interacting scalar fields, where the mass of the complex scalar field results from the interaction with the real scalar field which has a finite vacuum expectation value. We here study a new family of self-gravitating axially-symmetric, rotating boson stars in this model. In the flat space limit these boson stars tend to the corresponding Q-balls. Subject to the usual synchronization condition, the model admits spinning hairy black hole solutions with two different types of scalar hair. We here investigate parity-even and parity-odd boson stars and their associated hairy black holes. We explore the domain of existence of the solutions and address some of their physical properties. The solutions exhibit close similarity to the corresponding boson stars and Kerr black holes with synchronised scalar hair in the O(3)-sigma model coupled to Einstein gravity and to the corresponding solutions in the Einstein-Klein-Gordon theory with a complex scalar field, where the latter are recovered in a limit.

Obstructions towards a generalization of no-hair theorems: Scalar clouds around Kerr black holes

We show that the integral method used to prove the no-hair theorem for black holes (BH's) in spherically symmetric and static spacetimes within the framework of general relativity with matter composed by a complex-valued scalar-field does not lead to a straightforward conclusion about the absence of hair in the stationary and rotating (axisymmetric) scenario. We argue that such a failure can be used to justify in a simple and heuristic way the existence of nontrivial boson clouds or hair found numerically by Herdeiro and Radu [Phys. Rev. Lett. 112, 221101 (2014); Classical Quantum Gravity 32, 144001 (2015)] and analytically by Hod in the test field limit [Phys. Rev. D 86, 104026 (2012); Phys. Rev. D 86, 129902(E) (2012); Eur. Phys. J. C 73, 2378 (2013); J. High Energy Phys. 01 (2017) 030]. This is due to the presence of a contribution that is negative when rotation exists which allows for an integral to vanish even when a nontrivial boson hair is present. The presence of such a negative contribution that depends on the rotation properties of the BH is perfectly correlated with the eigenvalue problem associated with the boson-field equation. Conversely, when the rotation is absent the integral turns to be composed only by non negative (i.e., positive semidefinite) terms and thus the only way it can vanish is when the hair is completely absent. This analysis poses serious challenges and obstructions towards the elaboration of no-hair theorems for more general spacetimes endowed with a BH region even when including matter fields that obey the energy conditions. Thus rotating boson stars, if collapsed, may lead indeed to a new type of rotating BH, like the ones found in [Phys. Rev. Lett. 112, 221101 (2014); Classical Quantum Gravity 32, 144001 (2015)]. In order to achieve this analysis we solve numerically the eigenvalue problem for the boson field in the Kerr-BH background by imposing rigorous regularity conditions at the BH horizon for the non-extremal case ($0<a<M$) which include the near extremal one in the limit $M\ensuremath{\rightarrow}a$, as well as the small BH limit $M\ensuremath{\rightarrow}a\ensuremath{\rightarrow}0$.

Spinning boson stars and hairy black holes with nonminimal coupling

We obtain spinning boson star solutions and hairy black holes with synchronized hair in the Einstein–Klein–Gordon model, wherein the scalar field is massive, complex and with a nonminimal coupling to the Ricci scalar. The existence of these hairy black holes in this model provides yet another manifestation of the universality of the synchronization mechanism to endow spinning black holes with hair. We study the variation of the physical properties of the boson stars and hairy black holes with the coupling parameter between the scalar field and the curvature, showing that they are, qualitatively, identical to those in the minimally coupled case. By discussing the conformal transformation to the Einstein frame, we argue that the solutions herein provide new rotating boson star and hairy black hole solutions in the minimally coupled theory, with a particular potential, and that no spherically symmetric hairy black hole solutions exist in the nonminimally coupled theory, under a condition of conformal regularity.

Gravitational wave signatures of highly compact boson star binaries

Solitonic boson stars are stable objects made of a complex scalar field with a compactness that can reach values comparable to that of neutron stars. A recent study of the collision of identical boson stars produced only non-rotating boson stars or black holes, suggesting that rotating boson stars may not form from binary mergers. Here we extend this study to include an analysis of the gravitational waves radiated during the coalescence of such a binary, which is crucial to distinguish these events from other binaries with LIGO and Virgo observations. Our studies reveal that the remnant's gravitational wave signature is mainly governed by its fundamental frequency as it settles down to a non-rotating boson star, emitting significant gravitational radiation during this post-merger state. We calculate how the waveforms and their post-merger frequencies depend on the compactness of the initial boson stars and estimate analytically the amount of energy radiated after the merger.