Two Spinning Black Holes Balanced by Their Synchronized Scalar Hair.

General relativity minimally coupled to a massive, free, complex scalar field, is shown to allow asymptotically flat solutions, nonsingular on and outside the event horizon, describing two spinning black holes (2sBHs) in equilibrium, with coaxial, aligned angular momenta. The 2sBHs configurations bifurcate from solutions describing dipolar spinning boson stars. The BHs emerge at equilibrium points diagnosed by a test particle analysis and illustrated by a Newtonian analog. The individual BH "charges" are mass and angular momentum only. Equilibrium is due to the scalar environment, acting as a (compact) dipolar field, providing a lift against their mutual attraction, making the 2sBHs (h)airborne. We explore the 2sBHs domain of solutions and its main features.

Exotic Compact Objects and the Fate of the Light-Ring Instability.

Ultracompact objects with light rings (LRs) but without an event horizon could mimic black holes (BHs) in their strong gravity phenomenology. But are such objects dynamically viable? Stationary and axisymmetric ultracompact objects that can form from smooth, quasi-Minkowski initial data must have at least one stable LR, which has been argued to trigger a spacetime instability; but its development and fate have been unknown. Using fully nonlinear numerical evolutions of ultracompact bosonic stars free of any other known instabilities and introducing a novel adiabatic effective potential technique, we confirm the LRs triggered instability, identifying two possible fates: migration to nonultracompact configurations or collapse to BHs. In concrete examples we show that typical migration (collapse) timescales are not larger than ∼10^{3} light-crossing times, unless the stable LR potential well is very shallow. Our results show that the LR instability is effective in destroying horizonless ultracompact objects that could be plausible BH imitators.

Spin-Induced Scalarized Black Holes.

It was recently shown that a scalar field suitably coupled to the Gauss-Bonnet invariant G can undergo a spin-induced linear tachyonic instability near a Kerr black hole. This instability appears only once the dimensionless spin j is sufficiently large, that is, j≳0.5. A tachyonic instability is the hallmark of spontaneous scalarization. Focusing, for illustrative purposes, on a class of theories that do exhibit this instability, we show that stationary, rotating black hole solutions do indeed have scalar hair once the spin-induced instability threshold is exceeded, while black holes that lie below the threshold are described by the Kerr solution. Our results provide strong support for spin-induced black hole scalarization.

Multifield, Multifrequency Bosonic Stars and a Stabilization Mechanism.

Scalar bosonic stars (BSs) stand out as a multipurpose model of exotic compact objects. We enlarge the landscape of such (asymptotically flat, stationary, everywhere regular) objects by considering multiple fields (possibly) with different frequencies. This allows for new morphologies and a stabilization mechanism for different sorts of unstable BSs. First, any odd number of complex fields, yields a continuous family of BSs departing from the spherical, equal frequency, ℓ-BSs. As the simplest illustration, we construct the ℓ=1 BSs family, that includes several single-frequency solutions, including even parity (such as spinning BSs and a toroidal, static BS) and odd parity (a dipole BS) limits. Second, these limiting solutions are dynamically unstable, but can be stabilized by a hybrid-ℓ construction: adding a sufficiently large fundamental ℓ=0 BS of another field, with a different frequency. Evidence for this dynamical robustness is obtained by nonlinear numerical simulations of the corresponding Einstein-(complex, massive) Klein-Gordon system, both in formation and evolution scenarios, and a suggestive correlation between stability and energy distribution is observed. Similarities and differences with vector BSs are anticipated.

GW190521 as a Merger of Proca Stars: A Potential New Vector Boson of 8.7×10

Advanced LIGO-Virgo have reported a short gravitational-wave signal (GW190521) interpreted as a quasicircular merger of black holes, one at least populating the pair-instability supernova gap, that formed a remnant black hole of M_{f}∼142 M_{⊙} at a luminosity distance of d_{L}∼5.3 Gpc. With barely visible pre-merger emission, however, GW190521 merits further investigation of the pre-merger dynamics and even of the very nature of the colliding objects. We show that GW190521 is consistent with numerically simulated signals from head-on collisions of two (equal mass and spin) horizonless vector boson stars (aka Proca stars), forming a final black hole with M_{f}=231_{-17}^{+13} M_{⊙}, located at a distance of d_{L}=571_{-181}^{+348} Mpc. This provides the first demonstration of close degeneracy between these two theoretical models, for a real gravitational-wave event. The favored mass for the ultralight vector boson constituent of the Proca stars is µ_{V}=8.72_{-0.82}^{+0.73}×10^{-13} eV. Confirmation of the Proca star interpretation, which we find statistically slightly preferred, would provide the first evidence for a long sought dark matter particle.

Stationary Black Holes and Light Rings.

The ringdown and shadow of the astrophysically significant Kerr black hole (BH) are both intimately connected to a special set of bound null orbits known as light rings (LRs). Does it hold that a generic equilibrium BH must possess such orbits? In this Letter we prove the following theorem. A stationary, axisymmetric, asymptotically flat black hole spacetime in 1+3 dimensions, with a nonextremal, topologically spherical, Killing horizon admits, at least, one standard LR outside the horizon for each rotation sense. The proof relies on a topological argument and assumes C^{2} smoothness and circularity, but makes no use of the field equations. The argument is also adapted to recover a previous theorem establishing that a horizonless ultracompact object must admit an even number of nondegenerate LRs, one of which is stable.

Spontaneously Scalarized Kerr Black Holes in Extended Scalar-Tensor-Gauss-Bonnet Gravity.

We construct asymptotically flat, spinning, regular on and outside an event horizon, scalarized black holes (SBHs) in extended scalar-tensor-Gauss-Bonnet models. They reduce to Kerr BHs when the scalar field vanishes. For an illustrative choice of nonminimal coupling, we scan the domain of existence. For each value of spin, SBHs exist in an interval between two critical masses, with the lowest one vanishing in the static limit. Non-uniqueness with Kerr BHs of equal global charges is observed; the SBHs are entropically favoured. This suggests that SBHs form dynamically from the spontaneous scalarization of Kerr BHs, which are prone to a scalar-triggered tachyonic instability, below the largest critical mass. Phenomenologically, the introduction of BH spin damps the maximal observable difference between comparable scalarized and vacuum BHs. In the static limit, (perturbatively stable) SBHs can store over 20% of the spacetime energy outside the event horizon; in comparison with Schwarzschild BHs, their geodesic frequency at the ISCO can differ by a factor of 2.5 and deviations in the shadow areal radius may top 40%. As the BH spin grows, low mass SBHs are excluded, and the maximal relative differences decrease, becoming of the order of a few percent for dimensionless spin j≳0.5. This reveals a spin selection effect: non-GR effects are only significant for low spin. We discuss if and how the recently measured shadow size of the M87 supermassive BH constrains the length scale of the Gauss-Bonnet coupling.

Spontaneous Scalarization of Charged Black Holes.

Extended scalar-tensor Gauss-Bonnet (ESTGB) gravity has been recently argued to exhibit spontaneous scalarization of vacuum black holes (BHs). A similar phenomenon can be expected in a larger class of models, which includes, e.g., Einstein-Maxwell scalar (EMS) models, where spontaneous scalarization of electrovacuum BHs should occur. EMS models have no higher curvature corrections, a technical simplification over ESTGB models that allows us to investigate, fully nonlinearly, BH scalarization in two novel directions. First, numerical simulations in spherical symmetry show, dynamically, that Reissner-Nordström (RN) BHs evolve into a perturbatively stable scalarized BH. Second, we compute the nonspherical sector of static scalarized BH solutions bifurcating from the RN BH trunk. Scalarized BHs form an infinite (countable) number of branches and possess a large freedom in their multipole structure. Unlike the case of electrovacuum, the EMS model admits static, asymptotically flat, regular on and outside the horizon BHs without spherical symmetry and even without any spatial isometries, which are thermodynamically preferred over the electrovacuum state. We speculate on a possible dynamical role of these nonspherical scalarized BHs.

Dynamical Formation of Kerr Black Holes with Synchronized Hair: An Analytic Model.

East and Pretorius have successfully evolved, using fully nonlinear numerical simulations, the superradiant instability of the Kerr black hole (BH) triggered by a massive, complex vector field. Evolutions terminate in stationary states of a vector field condensate synchronized with a rotating BH horizon. We show that these end points are fundamental states of Kerr BHs with synchronized Proca hair. Motivated by the "experimental data" from these simulations, we suggest a universal (i.e., field-spin independent), analytic model for the subset of BHs with synchronized hair that possess a quasi-Kerr horizon, applicable in the weak hair regime. Comparing this model with fully nonlinear numerical solutions of BHs with a synchronized scalar or Proca hair, we show that the model is accurate for hairy BHs that may emerge dynamically from superradiance, whose domain we identify.

Light-Ring Stability for Ultracompact Objects.

We prove the following theorem: axisymmetric, stationary solutions of the Einstein field equations formed from classical gravitational collapse of matter obeying the null energy condition, that are everywhere smooth and ultracompact (i.e., they have a light ring) must have at least two light rings, and one of them is stable. It has been argued that stable light rings generally lead to nonlinear spacetime instabilities. Our result implies that smooth, physically and dynamically reasonable ultracompact objects are not viable as observational alternatives to black holes whenever these instabilities occur on astrophysically short time scales. The proof of the theorem has two parts: (i) We show that light rings always come in pairs, one being a saddle point and the other a local extremum of an effective potential. This result follows from a topological argument based on the Brouwer degree of a continuous map, with no assumptions on the spacetime dynamics, and, hence, it is applicable to any metric gravity theory where photons follow null geodesics. (ii) Assuming Einstein's equations, we show that the extremum is a local minimum of the potential (i.e., a stable light ring) if the energy-momentum tensor satisfies the null energy condition.

Static Einstein-Maxwell Black Holes with No Spatial Isometries in AdS Space.

We explicitly construct static black hole solutions to the fully nonlinear, D=4, Einstein-Maxwell-anti-de Sitter (AdS) equations that have no continuous spatial symmetries. These black holes have a smooth, topologically spherical horizon (section), but without isometries, and approach, asymptotically, global AdS spacetime. They are interpreted as bound states of a horizon with the Einstein-Maxwell-AdS solitons recently discovered, for appropriate boundary data. In sharp contrast to the uniqueness results for a Minkowski electrovacuum, the existence of these black holes shows that single, equilibrium, black hole solutions in an AdS electrovacuum admit an arbitrary multipole structure.

Explosion and Final State of an Unstable Reissner-Nordström Black Hole.

A Reissner-Nordström black hole (BH) is superradiantly unstable against spherical perturbations of a charged scalar field enclosed in a cavity, with a frequency lower than a critical value. We use numerical relativity techniques to follow the development of this unstable system-dubbed a charged BH bomb-into the nonlinear regime, solving the full Einstein-Maxwell-Klein-Gordon equations, in spherical symmetry. We show that (i) the process stops before all the charge is extracted from the BH, and (ii) the system settles down into a hairy BH: a charged horizon in equilibrium with a scalar field condensate, whose phase is oscillating at the (final) critical frequency. For a low scalar field charge q, the final state is approached smoothly and monotonically. For large q, however, the energy extraction overshoots, and an explosive phenomenon, akin to a bosenova, pushes some energy back into the BH. The charge extraction, by contrast, does not reverse.

Shadows of Kerr Black Holes with Scalar Hair.

Using backwards ray tracing, we study the shadows of Kerr black holes with scalar hair (KBHSH). KBHSH interpolate continuously between Kerr BHs and boson stars (BSs), so we start by investigating the lensing of light due to BSs. Moving from the weak to the strong gravity region, BSs-which by themselves have no shadows-are classified, according to the lensing produced, as (i) noncompact, which yield not multiple images, (ii) compact, which produce an increasing number of Einstein rings and multiple images of the whole celestial sphere, and (iii) ultracompact, which possess light rings, yielding an infinite number of images with (we conjecture) a self-similar structure. The shadows of KBHSH, for Kerr-like horizons and noncompact BS-like hair, are analogous to, but distinguishable from, those of comparable Kerr BHs. But for non-Kerr-like horizons and ultracompact BS-like hair, the shadows of KBHSH are drastically different: novel shapes arise, sizes are considerably smaller, and multiple shadows of a single BH become possible. Thus, KBHSH provide quantitatively and qualitatively new templates for ongoing (and future) very large baseline interferometry observations of BH shadows, such as those of the Event Horizon Telescope.

Exploring New Physics Frontiers Through Numerical Relativity.

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology.

Kerr black holes with scalar hair.

We present a family of solutions of Einstein's gravity minimally coupled to a complex, massive scalar field, describing asymptotically flat, spinning black holes with scalar hair and a regular horizon. These hairy black holes (HBHs) are supported by rotation and have no static limit. Besides mass M and angular momentum J, they carry a conserved, continuous Noether charge Q measuring the scalar hair. HBHs branch off from the Kerr metric at the threshold of the superradiant instability and reduce to spinning boson stars in the limit of vanishing horizon area. They overlap with Kerr black holes for a set of (M, J) values. A single Killing vector field preserves the solutions, tangent to the null geodesic generators of the event horizon. HBHs can exhibit sharp physical differences when compared to the Kerr solution, such as J/M^{2}>1, a quadrupole moment larger than J^{2}/M, and a larger orbital angular velocity at the innermost stable circular orbit. Families of HBHs connected to the Kerr geometry should exist in scalar (and other) models with more general self-interactions.

Universe-inspired algorithms for control engineering: A review.

Control algorithms have been proposed based on knowledge related to nature-inspired mechanisms, including those based on the behavior of living beings. This paper presents a review focused on major breakthroughs carried out in the scope of applied control inspired by the gravitational attraction between bodies. A control approach focused on Artificial Potential Fields was identified, as well as four optimization metaheuristics: Gravitational Search Algorithm, Black-Hole algorithm, Multi-Verse Optimizer, and Galactic Swarm Optimization. A thorough analysis of ninety-one relevant papers was carried out to highlight their performance and to identify the gravitational and attraction foundations, as well as the universe laws supporting them. Included are their standard formulations, as well as their improved, modified, hybrid, cascade, fuzzy, chaotic and adaptive versions. Moreover, this review also deeply delves into the impact of universe-inspired algorithms on control problems of dynamic systems, providing an extensive list of control-related applications, and their inherent advantages and limitations. Strong evidence suggests that gravitation-inspired and black-hole dynamic-driven algorithms can outperform other well-known algorithms in control engineering, even though they have not been designed according to realistic astrophysical phenomena and formulated according to astrophysics laws. Even so, they support future research directions towards the development of high-sophisticated control laws inspired by Newtonian/Einsteinian physics, such that effective control-astrophysics bridges can be established and applied in a wide range of applications.

Radiation from a D-dimensional collision of shock waves: a remarkably simple fit formula.

Recently we estimated the energy radiated in the head-on collision of two equal D-dimensional Aichelburg-Sexl shock waves, for even D, by solving perturbatively, to first order, the Einstein equations in the future of the collision. Here, we report on the solution for the odd D case. After finding the wave forms, we extract the estimated radiated energy for D=5, 7, 9, and 11 and unveil a remarkably simple pattern, given the complexity of the framework: (for all D) the estimated fraction of radiated energy matches the analytic expression 1/2-1/D, within the numerical error (less than 0.1%). Both this fit and the apparent horizon bound converge to 1/2 as D→∞.