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

What does a black hole look like? In 1 + 3 spacetime dimensions, the optical appearance of a black hole is a bidimensional region in the observer’s sky often called the black hole shadow, as supported by the EHT observations. In higher dimensions this question is more subtle and observational setup dependent. Previous studies considered the shadows of higher dimensional black holes to remain bidimensional. We argue that the latter should be regarded as a tomography of a higher dimensional structure, the $\textit{hypershadow}$, which would be the structure “seen” by higher dimensional observers. As a case study we consider the cohomogeneity-one Myers-Perry black hole in 1 + 4 dimensions, and compute its tridimensional hypershadow.

João Novo

Pedro Cunha

Hypershadows of higher dimensional black objects: a case study of cohomogeneity-one d=5 Myers-Perry

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

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

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.

Spain

Jose Blázquez-Salcedo

Sarah Kahlen

Alexandre Pombo

Quasinormal modes of hot, cold and bald Einstein–Maxwell-scalar black holes

Obtaining solutions of the Einstein field equations describing spinning compact bodies is typically challenging. The Newman–Janis algorithm provides a procedure to obtain rotating spacetimes from a static, spherically symmetric, seed metric. It is not guaranteed, however, that the resulting rotating spacetime solves the same field equations as the seed. Moreover, the former may not be circular, and thus expressible in Boyer–Lindquist-like coordinates. Amongst the variations of the original procedure, a modified Newman–Janis algorithm (MNJA) has been proposed that, by construction, originates a circular, spinning spacetime, expressible in Boyer–Lindquist-like coordinates. As a down side, the procedure introduces an ambiguity, that requires extra assumptions on the matter content of the model. In this paper we observe that the rotating spacetimes obtained through the MNJA always admit separability of the Hamilton–Jacobi equation for the case of null geodesics, in which case, moreover, the aforementioned ambiguity has no impact, since it amounts to an overall metric conformal factor. We also show that the Hamilton–Jacobi equation for light rays propagating in a plasma admits separability if the plasma frequency obeys a certain constraint. As an illustration, we compute the shadow and lensing of some spinning black holes obtained by the MNJA.

Brazil

Haroldo Junior

Luís Crispino

Spinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithm

In the simplest scalar-tensor theories, wherein the scalar field is non-minimally coupled to the Ricci scalar, spontaneous scalarization of electrovacuum black holes (BHs) does not occur. This ceases to be true in higher dimensional spacetimes, d &gt; 4. We consider the scalarization of the higher dimensional Reissner-Nordström BHs in scalar-tensor models and provide results on the zero modes for different d, together with an explicit construction of the scalarized BHs in d = 5, discussing some of their properties. We also observe that a conformal transformation into the Einstein frame maps this model into an Einstein-Maxwel- scalar model, wherein the non-minimal coupling occurs between the scalar field and the Maxwell invariant (rather than the Ricci scalar), thus relating the occurence of scalarization in the two models. Next, we consider the spontaneous scalarization of the Schwarzschild- Tangherlini BH in extended-scalar-tensor-Lovelock gravity in even dimensions. In these models, the scalar field is non-minimally coupled to the (d/2) th  Euler density, in d spacetime dimensions. We construct explicitly examples in d = 6, 8, showing the properties of the four dimensional case are qualitatively generic, but with quantitative differences. We compare these higher d scalarized BHs with the hairy BHs in shift-symmetric Horndeski theory, for the same d, which we also construct.

Chile

Dumitru Astefanesei

João Oliveira

Higher dimensional black hole scalarization

Electromagnetic duality is discussed in the context of Einstein-Maxwell-scalar (EMS) models including axionic-type couplings. This family of models introduces two non-minimal coupling functions f(ϕ) and g(ϕ), depending on a real scalar field ϕ. Interpreting the scalar field as a medium, one naturally defines constitutive relations as in relativistic non-linear electrodynamics. Requiring these constitutive relations to be invariant under the SO(2) electromagnetic duality rotations of Maxwell’s theory, defines 1-parameter, closed duality orbits in the space of EMS models, connecting different electromagnetic fields in “dual” models with different coupling functions, but leaving both the scalar field and the spacetime geometry invariant. This mapping works as a solution generating technique, extending any given solution of a specific model to a (different) solution for any of the dual models along the whole duality orbit. We illustrate this technique by considering the duality orbits seeded by specific EMS models wherein solitonic and black hole solutions are known. For dilatonic models, specific rotations are equivalent to S-duality.

Electromagnetic dual Einstein-Maxwell-scalar models

We consider Einstein-Maxwell-dilaton gravity with the non-minimal exponential coupling between the dilaton and the Maxwell field emerging from low energy heterotic string theory. The dilaton is endowed with a potential that originates from an electromagnetic Fayet-Iliopoulos (FI) term in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 extended supergravity in four spacetime dimensions. For the case we are interested in, this potential introduces a single parameter α. When α → 0, the static black holes (BHs) of the model are the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) solutions. When α → ∞, the BHs become the standard Reissner-Nordström (RN) solutions of electrovacuum General Relativity. The BH solutions for finite non-zero α interpolate between these two families. In this case, the dilaton potential regularizes the extremal limit of the GMGHS solution yielding a set of zero temperature BHs with a near horizon AdS 2 × S 2 geometry. We show that, in the neighborhood of these extremal solutions, there is a subset of BHs that are dynamically and thermodynamically stable, all of which have charge to mass ratio larger than unity. By dynamical stability we mean that no growing quasi-normal modes are found; thus they are stable against linear perturbations (spherical and non-spherical). Moreover, non-linear numerical evolutions lend support to their non-linear stability. By thermodynamical stability we mean the BHs are stable both in the canonical and grand-canonical ensemble. In particular, both the specific heat at constant charge and the isothermal permittivity are positive. This is not possible for RN and GMGHS BHs. We discuss the different thermodynamical phases for the BHs in this model and comment on what may allow the existence of both dynamically and thermodynamically stable BHs.