We study the bifurcation phenomena between spherical and axisymmetric bosonic stars. By numerically solving for the zero-modes of spherical bosonic stars under specific axially symmetric perturbations, we discover that excited state spherical bosonic stars bifurcate into two types of axisymmetric bosonic stars under = 2 perturbations, with matter distributions resembling chains and rings, respectively. Meanwhile, = 4 axisymmetric perturbations lead spherical scalar bosonic stars to bifurcate into a new type of axisymmetric bosonic stars, exhibiting a mixed chain-like and ring-like matter distribution, which we refer to as gyroscope-like. Additionally, for the first time, we have constructed chains of scalar bosonic stars with 7 constituents and their corresponding ring-like scalar bosonic stars. Our results provide an explanation for the bifurcations in bosonic stars from the perspective of perturbations, and by analyzing physical quantities such as quadrupoles and energy densities we systematically discuss the impact of axisymmetric perturbations on spherical bosonic stars.

Portugal

Chen Liang

Carlos Herdeiro

Eugen Radu

Bifurcations in bosonic stars: chains and rings from spherical solutions

We consider a model with two real Maxwell fields (or equivalently, a complex Maxwell field) minimally coupled to Einstein's gravity with a negative cosmological constant in four spacetime dimensions. Assuming a specific harmonic dependence of the vector fields, we show the existence of asymptotically anti-de Sitter (AdS) self-gravitating boson-star–like solitonic solutions, which are static and axially symmetric. Analytical solutions are found in the test-field limit, where the Maxwell equations are solved on a fixed AdS background. The fully nonlinear solutions are constructed numerically.

China

Germany

Hyat Huang

Jutta Kunz

Einstein-(complex)-Maxwell static boson stars in AdS

For gauged scalar fields minimally coupled to Einstein-Maxwell theory, the Mayo-Bekenstein no-hair theorem can be circumvented when including appropriate scalar self-interactions, allowing static, electrically charged black holes to be endowed with (Abelian) gauged scalar hair. Here we show these spherically symmetric solutions can be extended to include a magnetic charge in a model with scalar multiplets. The resulting dyonic configurations share most of the properties of the electrically charged solutions, in particular satisfying the same resonance condition, with the existence of a mass gap with respect to the bald Reissner-Nordström dyonic black holes. A distinctive feature, however, is that no solitonic limit exists for a non-zero magnetic charge.

JINR

Yakov Shnir

Reissner-Nordström dyonic black holes with gauged scalar hair

We consider an Einstein-scalar field model which is a consistent truncation of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 8 D = 4 gauged supergravity, the scalar field possessing a potential which is unbounded from below and a tachyonic mass above the Breitenlohner-Freedman bound. We investigate the spherically symmetric asymptotically anti-de Sitter soliton and black hole solutions, with the aim of clarifying the asymptotics and the possible boundary conditions at infinity. The emerging picture is contrasted with that found for an Einstein-scalar field model with the same scalar mass and a quartic selfinteraction term. We also provide arguments for the existence of solitonic solutions which can be viewed as non-linear continuation of the (probe) scalar multipolar clouds, with emphasis on the dipole case. Apart from numerical results, exact solutions are found for solitons with a monopole and dipole scalar field, as perturbations around the AdS background.

Chile

Dumitru Astefanesei

Einstein-scalar field solutions in AdS spacetime: clouds, boundary conditions, and scalar multipoles

In the presence of certain non-minimal couplings between a scalar field and the Gauss-Bonnet curvature invariant, Kerr black holes can scalarize, as long as they are spinning fast enough. This provides a distinctive violation of the Kerr hypothesis, occurring only for some high spin range. In this paper we assess if strong magnetic fields, that may exist in the vicinity of astrophysical black holes, could facilitate this distinctive effect, by bringing down the spin threshold for scalarization. This inquiry is motivated by the fact that self-gravitating magnetic fields, by themselves, can also promote “spin-induced” scalarization. Nonetheless, we show that in the vicinity of the horizon the effect of the magnetic field B on a BH of mass M, up to <math><mi>B</mi><mi>M</mi><mo>≲</mo><mn>1</mn></math>, works against spin-induced scalarization, requiring a larger dimensionless spin j from the black hole. A geometric interpretation for this result is suggested, in terms of the effects of rotation vs. magnetic fields on the horizon geometry.

Lorenzo Annulli

Carlos A.R. Herdeiro

Spin-induced scalarization and magnetic fields

The Ellis-Bronnikov solution provides a simple toy model for the study of various aspects of wormhole physics. In this work we solve the Klein-Gordon equation in this background and find an exact solution in terms of Heun's function. This may describe ‘scalar clouds’ (<math><mi>i</mi><mo>.</mo><mi>e</mi></math>. localized, particle-like configuration) or scalar waves. However, in the former case, the radial derivative of the scalar field is discontinuous at the wormhole's throat (except for the spherical case). This pathology is absent for a suitable scalar field self-interaction, and we provide evidence for the existence of spherically symmetric and spinning Q-balls in a Ellis-Bronnikov wormhole background.

Spain

Jose Luis Blázquez-Salcedo

Romania

Marina-Aura Dariescu

Ciprian Dariescu

Cristian Stelea

Probing the Ellis-Bronnikov wormhole geometry with a scalar field: Clouds, waves and Q-balls

The possibility of mining the rotational energy from black holes has far–reaching implications. Such energy extraction could occur even for isolated black holes, if hypothetical ultralight bosonic particles exist in Nature, leading to a new equilibrium state – a black hole with synchronised bosonic hair – whose lifetime could exceed the age of the Universe. A natural question is then: for an isolated black hole and at maximal efficiency, how large is the energy fraction ϵ that can be extracted from a Kerr black hole by the superradiant growth of the dominant mode? In other words, how hairy can the resulting black hole become? A thermodynamical bound for the total superradiance efficiency, <math><mi>ϵ</mi><mo>≲</mo><mn>0.29</mn></math> (as a fraction of the initial black hole mass), has long been known, from the area law. However, numerical simulations exhibiting the growth of the dominant mode only reached about one third of this value. We show that if the development of superradiant instabilities is approximately conservative (as suggest by the numerical evolutions), this efficiency is limited to <math><mi>ϵ</mi><mo>≲</mo><mn>0.10</mn></math>, regardless of the spin of the bosonic field. This is in agreement with the maximum energy extraction obtained in numerical simulations for a vector field and predicts the result of similar simulations with a scalar field, yet to be performed.

Nuno M. Santos

A bound on energy extraction (and hairiness) from superradiance

The Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black hole is an influential solution of the low energy heterotic string theory. As it is well known, it presents a singular extremal limit. We construct a regular extension of the GMGHS extremal black hole in a model with <math><mi>O</mi><mo>(</mo><msup><mrow><mi>α</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></math> corrections in the action, by solving the fully non-linear equations of motion. The de-singularization is supported by the <math><mi>O</mi><mo>(</mo><msup><mrow><mi>α</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></math>-terms. The regularised extremal GMGHS BHs are asymptotically flat, possess a regular (non-zero size) horizon of spherical topology, with an <math><mi>A</mi><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math> near horizon geometry, and their entropy is proportional to the electric charge. The near horizon solution is obtained analytically and some illustrative bulk solutions are constructed numerically.

Japan

Kunihito Uzawa

De-singularizing the extremal GMGHS black hole via higher derivatives corrections

We study an Abelian gauged <math><mi>O</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> Skyrme model in <math><mn>4</mn><mo>+</mo><mn>1</mn></math> dimensions, featuring the <math><msup><mrow><mi>F</mi></mrow><mrow><mn>4</mn></mrow></msup></math> Maxwell and the Chern-Simons terms. Our aim is to expose the mechanism, discovered in the analogous Abelian gauged <math><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> Skyrme model in <math><mn>2</mn><mo>+</mo><mn>1</mn></math> dimensions, which leads to the unusual relation of the mass-energy E to the electric charge <math><msub><mrow><mi>Q</mi></mrow><mrow><mi>e</mi></mrow></msub></math> and angular momentum J, and, to the change in the value of the “baryon number” q due to the influence of the Abelian field on the Skyrmion. Chern-Simons dynamics together with the dynamics of the gauged Skyrme scalar, allows for solutions with varying asymptotic values of the magnetic field, resulting in these unusual properties listed. Numerical work is carried out on an effective one dimensional subsystem resulting from imposition of an enhanced radial symmetry on <math><msup><mrow><mi>R</mi></mrow><mrow><mn>4</mn></mrow></msup></math>.

Francisco Navarro-Lérida

Ireland

D.H. Tchrakian

On the effects of the Chern-Simons term in an Abelian gauged Skyrme model in = 4 + 1 Dimensions

Einstein–Maxwell-scalar models allow for different classes of black hole solutions, depending on the non-minimal coupling function  $$f(\phi )$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>ϕ</mi> <mo>)</mo> </mrow> </math>   employed, between the scalar field and the Maxwell invariant. Here, we address the linear mode stability of the black hole solutions obtained recently for a quartic coupling function,  $$f(\phi )=1+\alpha \phi ^4$$  <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>ϕ</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mi>α</mi> <msup> <mi>ϕ</mi> <mn>4</mn> </msup> </mrow> </math>   (Blázquez-Salcedo et al. in Phys. Lett. B 806:135493, 2020). Besides the bald Reissner–Nordström solutions, this coupling allows for two branches of scalarized black holes, termed cold and hot, respectively. For these three branches of black holes we calculate the spectrum of quasinormal modes. It consists of polar scalar-led modes, polar and axial electromagnetic-led modes, and polar and axial gravitational-led modes. We demonstrate that the only unstable mode present is the radial scalar-led mode of the cold branch. Consequently, the bald Reissner–Nordström branch and the hot scalarized branch are both mode-stable. The non-trivial scalar field in the scalarized background solutions leads to the breaking of the degeneracy between axial and polar modes present for Reissner–Nordström solutions. This isospectrality is only slightly broken on the cold branch, but it is strongly broken on the hot branch.