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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 $\ell=2$ perturbations, with matter distributions resembling chains and rings, respectively. Meanwhile, $\ell=4$ 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., Comment: 21 pages, 8 figures

We study stationary clouds of a gauged, complex scalar field on a magnetically (and possibly electrically as well) charged Kerr-Newman black hole (BH). The existence of a magnetic charge $Q_m$ promotes a north-south $\textit{asymmetry}$ of the scalar clouds. This breakdown of the clouds' $\mathbb{Z}_2$-symmetry carries through to the spacetime $\textit{geometry}$ for the non-linear continuation of the clouds: a family of magnetically charged (or dyonic) BHs with synchronized gauged scalar hair, which we construct. Their distinct phenomenology is illustrated by their imaging, exhibiting skewed shadows and lensing. Such hairy BHs could, in principle, result from the superradiant instability of magnetically charged Kerr-Newman BHs, unveiling a dynamical mechanism for creating north-south asymmetric BHs from standard $\mathbb{Z}_2$-symmetric electrovacuum BHs., Comment: 19 pages, 10 figures

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 {\it resonance} condition, with the existence of a mass gap with respect to the bald Reissner-Nordstr\"om dyonic black holes. A distinctive feature, however, is that no solitonic limit exists for a non-zero magnetic charge., Comment: 12 pages, 5 figures

Recently, spherical and static flat space solitons (balls) and self-gravitating, everywhere regular, asymptotically flat solitons (stars) were constructed in an Einstein-Proca-Higgs model [1], where a complex vector field gains mass by coupling to a real scalar field with a Higgs-type potential. The Proca-Higgs model serves as a UV completion of a complex Proca model with self-interactions. Here, we construct and examine the mathematical and physical properties of rotating configurations. In particular, rotation allows horizon-bearing solutions, including stationary clouds surrounding Kerr black holes and their non-linear continuation into black holes with Proca-Higgs hair., Comment: 57 pages

We consider a model with two real Maxwell fields (or equivalently, a complex Maxwell field) minimally coupled to Einsteins 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., Comment: 13 pages, 2 figures

We present several high-accuracy surrogate models for gravitational-wave signals from equal-mass head-on mergers of Proca stars, computed through the Newman-Penrose scalar $\psi_4$. We also discuss the current state of the model extensions to mergers of Proca stars with different masses, and the particular challenges that these present. The models are divided in two main categories: two-stage and monolithic. In the two-stage models, a dimensional reduction algorithm is applied to embed the data in a reduced feature space, which is then interpolated in terms of the physical parameters. For the monolithic models, a single neural network is trained to predict the waveform from the input physical parameter. Our model displays mismatches below $10^{-3}$ with respect to the original numerical waveforms. Finally, we demonstrate the usage of our model in full Bayesian parameter inference through the accurate recovery of numerical relativity signals injected in zero-noise, together with the analysis of GW190521. For the latter, we observe excellent agreement with existing results that make use of full numerical relativity., Comment: 16 pages, 14 figures. v2: Matches published version

We analyse the lensing images by dynamically robust rotating (mini-)Proca stars surrounded by thin accretion disks. Due to their peculiar geodesic structure we show that these images exhibit striking similarities with the ones of BHs, for appropriately chosen disk intensity profile, when imposing a GRMHD-motivated emission cut off. Additionally, and unlike the non-rotating case, these similarities prevail even when considering equatorial observations. This example illustrates how a horizonless compact object without light rings, with a plausible formation mechanism and dynamically robust, could mimic detailed features of black hole imagiology., Comment: 23 pages, 11 figures + appendix

We construct a new family of rotating black holes with scalar hair and a regular horizon of spherical topology, within five dimensional ($d=5$) Einstein's gravity minimally coupled to a complex, massive scalar field doublet. These solutions represent generalizations of the Kaluza-Klein monopole found by Gross, Perry and Sorkin, with a twisted $S^1$ bundle over a four dimensional Minkowski spacetime being approached in the far field. The black holes are described by their mass, angular momentum, tension and a conserved Noether charge measuring the hairiness of the configurations. They are supported by rotation and have no static limit, while for vanishing horizon size, they reduce to boson stars. When performing a Kaluza-Klein reduction, the $d=5$ solutions yield a family of $d=4$ spherically symmetric dyonic black holes with gauged scalar hair. This provides a link between two seemingly unrelated mechanisms to endow a black hole with scalar hair: the $d=5$ synchronization condition between the scalar field frequency and the event horizon angular velocity results in the $d=4$ resonance condition between the scalar field frequency and the electrostatic chemical potential.

We study the Skyrmion of the $SO(2)$ gauged $O(3)$ sigma model in $2+1$ dimensions in the presence of a Skyrme--Chern-Simons (SCS) term, and compare its properties with the corresponding properties of the Skyrmion in the presence of the usual Chern-Simons (CS) term. We find that these properties are qualitatively largely similar in both cases, meaning that the SCS density can be employed as an alternative to the CS term also in higher dimensions, most importantly in even dimensions where no CS term is defined, $e.g.,$ in $3+1$ dimensions. The SCS density employed here is defined in terms of the pair of $SO(2)\times SO(2)$ gauge fields and an auxiliary $O(5)$ Skyrme scalar, which is contracted to an effective $O(3)$ Skyrme scalar. Technically, this study maps the methods to be applied in higher dimensional examples., Comment: 26 pages, 10 figures

We construct and dynamically evolve dipolar, self-interacting scalar boson stars in a model with sextic (+ quartic) self-interactions. The domain of existence of such dipolar $Q$-stars has a similar structure to that of the fundamental monopolar stars of the same model. For the latter it is structured in a Newtonian plus a relativistic branch, wherein perturbatively stable solutions exist, connected by a middle unstable branch. Our evolutions support similar dynamical properties of the dipolar $Q$-stars that: 1) in the Newtonian and relativistic branches are dynamically robust over time scales longer than those for which dipolar stars without self-interactions are seen to decay; 2) in the middle branch migrate to either the Newtonian or the relativistic branch; 3) beyond the relativistic branch decay to black holes. Overall, these results strengthen the observation, seen in other contexts, that self-interactions can mitigate dynamical instabilities of scalar boson star models., Comment: 13 pages, 14 figures; movies of the numerical simulations reported can be found in http://gravitation.web.ua.pt/index.php/node/4488

General Relativity minimally coupled to a massive, free, complex scalar field, is shown to allow asymptotically flat solutions, non-singular on and outside the event horizon, describing two spinning black holes (2sBHs) in equilibrium, with co-axial, 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 analogue. 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., Comment: 5 pages, 5 figures

We study extreme mass ratio inspirals (EMRIs) due to an infalling Light Compact Object (LCO) onto a generic class of stationary and axi-symmetric massive compact objects (MCO - with or without a horizon). Using the quadrupole hybrid formalism we obtain a master formula for the evolution of the radius of the LCO and find qualitatively different behaviours depending on the geodesic structure of the MCO. We then specialize the MCO to a black hole with synchronised scalar hair (BHsSH). To allow a comparison with a highly spinning Kerr BH, we consider BHsSH with dimensionless spin, $j = 1$. This yields two distinct sequences of solutions. The first harbours Kerr-like solutions with maximal hairiness of $\sim 10\%$. The corresponding EMRIs are Kerr-like, but the cut-off frequency can be a few times smaller than in Kerr, yielding waveforms with quantitatively significant non-Kerrness. The second sequence links the extremal Kerr black hole to a mini-boson star with $j=1$. Here we observe qualitative non-Kerrness, such as the non-monotonically increase of the angular velocity and stagnation endpoints, reflecting Kerr-unlike geodesic structures., Comment: 20 pages, 15 figures

We consider axially symmetric solutions of the U(1) gauged Skyrme model supplemented with a Callan-Witten (CW) anomaly density term. The main properties of the solutions are studied, several specific features introduced by the presence of the CW term being identified. We find that the solitons possess a nonzero angular momentum proportional to the electric charge, which in addition to the usual Coulomb part, acquires an extra (topological) contribution from the CW term. Specifically, it is shown that the slope of mass/energy $M$ $vs.$ electric charge $Q_e$ and angular momentum $J$ can be both positive $and$ negative. Furthermore, it is shown that the gauged Skyrmion persists even when the quartic (Skyrme) kinetic term disappears., Comment: 25 pages, 3 figures

We consider several different classes of asymptotically flat, rotating black objects in d = 5 Einstein-Gauss-Bonnet (EGB) theory. These are first the black holes with two equal-magnitude angular momenta, in which case extremal configurations are studied as well. Numerical evidence is also given for the existence of EGB generalizations of the Myers-Perry black holes with a single plane of rotation and of the Emparan-Reall balanced black rings. All solutions approach asymptotically the Minkowski background and present no singularities outside and on the horizon. The numerical results suggest that for any mass of the solutions and any topology of the horizon, the rotating configurations exist up to a maximal value of the GB coupling constant, while the solutions with a spherical horizon topology still satisfy the Einstein gravity bound on angular momentum., Comment: 14 pages, 2 figures; accepted for publication in Universe (Special Issue "Black Holes in Einstein-Gauss-Bonnet Theories")

We study the time evolution of spherical, excited -- with $n$ radial nodes -- scalar boson stars in General Relativity minimally coupled to a complex massive scalar field with quartic self-interactions. We report that these stars, with up to $n=10$, can be made dynamically stable, up to timescales of $t\sim\frac{10^{4}}{c\mu}$, where $\mu$ is the inverse Compton wavelength of the scalar particle, for sufficiently large values of the self-interactions coupling constant $\lambda$, which depend on $n$. We observe that the compactness of these solutions is rather insensitive to $n$, for large $\lambda$ and fixed frequency. Generically, along the branches where stability was studied, these excited boson stars are not compact enough to allow for innermost stable circular orbits or light rings. Finally, we discuss the angular velocity of particles along timelike circular orbits, suggesting an application, for solutions in the Newtonian limit, to galactic rotation curves., Comment: 16 pages, 16 figures, updated with an appendix to match published version

We show that, unlike vacuum General Relativity, Einstein-scalar theories allow balanced static, neutral, asymptotically flat, double-black hole solutions, for scalar field models minimally coupled to gravity, with appropriate self-interactions. These are scalar hairy versions of the double-Schwarzschild (or Bach-Weyl) solution, but regular on and outside the two (topologically spherical) horizons. The balancing repulsive force is provided by the scalar field. An explicit illustration is presented, using a Weyl-type construction adapted to numerical solutions, requiring no partial linearisation, or integrability structure, of the Einstein-scalar equations. Fixing the couplings of the model, the balanced configurationsform a one-parameter family of solutions, labelled by the proper distance between the black holes., Comment: 22 pages, 8 figures

We consider soliton solutions of the U(1) gauged Skyrme model with the pion mass term. The domain of existence of gauged Skyrmions is restricted from above by the value of the pion mass. Concentrating on the solutions of topological degree one, we find that coupling to the electromagnetic field breaks the symmetry of the configurations, the Skyrmions carrying both an electric charge and a magnetic flux, with an induced dipole magnetic moment. The Skyrmions also possess an angular momentum, which is quantized in the units of the electric charge. The mass of the gauged Skyrmions monotonically decreases with increase of the gauge coupling., Comment: 17 pages, 6 figures

We present a numerical study of relativistic Bondi-Hoyle-Lyttleton (BHL) accretion onto an asymptotically flat black hole with synchronized hair. The hair is sourced by an ultralight, complex scalar field, minimally coupled to Einstein's gravity. Our simulations consider a supersonic flow parametrized by the asymptotic values of the fluid quantities and a sample of hairy black holes with different masses, angular momenta, and amount of scalar hair. For all models, steady-state BHL accretion solutions are attained that are characterized by the presence of a shock-cone and a stagnation point downstream. For the models of the sample with the largest component of scalar field, the shock-cone envelops fully the black hole, transitioning into a bow-shock, and the stagnation points move further away downstream. Analytical expressions for the mass accretion rates are obtained after fitting the numerical results, which can be used to analyze black-hole formation scenarios in the presence of ultralight scalar fields. The formation of a shock-cone leads to regions where sound waves can be trapped and resonant oscillations excited. We measure the frequencies of such quasi-periodic oscillations and point out a possible association with quasi-periodic oscillations in the X-ray light curve of Sgr~A* and microquasars., Comment: 24 pages, 3 tables, 10 figures. Minor changes

We consider a Proca-Higgs model wherein a complex vector field gains mass via spontaneous symmetry breaking, by coupling to a real scalar field with a Higgs-type potential. This vector version of the scalar Friedberg-Lee-Sirlin model, can be considered as a UV completion of a complex Proca model with self-interactions. We study the flat spacetime and self-gravitating solitons of the model, that we dub Proca-Higgs \textit{balls} and \textit{stars} respectively, exploring the domain of solutions and describing some of their mathematical and physical properties. The stars reduce to the well-known (mini-)Proca stars in some limits. The full model evades the hyperbolicity problems of the self-interacting Proca models, offering novel possibilities for dynamical studies beyond mini-Proca stars.

We consider an Einstein-scalar field model which is a consistent truncation of ${\cal N}=8$ $D=4$ 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 self-interaction 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., Comment: 36 pages, 13 figures, Comments welcome

We investigate the gravitational lensing by spinning Proca stars and the shadows and lensing by Kerr black holes (BHs) with synchronised Proca hair, discussing both theoretical aspects and observational constraints from the Event Horizon Telescope (EHT) M87* and Sgr A* data. On the theoretical side, this family of BHs interpolates between Kerr-like solutions -- exhibiting a similar optical appearance to that of Kerr BHs -- to very non-Kerr like solutions, exhibiting exotic features such as cuspy shadows, egg-like shadows and ghost shadows. We interpret these features in terms of the structure of the fundamental photon orbits, for which different branches exist, containing both stable and unstable orbits, with some of the latter not being shadow related. On the observational side, we show that current EHT constraints are compatible with all such BHs that could form from the growth of the superradiant instability of Kerr BHs. Unexpectedly, given the (roughly) 10% error bars in the EHT data -- and in contrast to their scalar cousin model --, some of the BHs with up to 40% of their energy in their Proca hair are compatible with the current data. We estimate the necessary resolution of future observations to better constrain this model., Comment: 36 pages, 20 figures + appendix

We present a systematic study of the dynamics and gravitational-wave emission of head-on collisions of spinning vector boson stars, known as Proca stars. To this aim we build a catalogue of about 800 numerical-relativity simulations of such systems. We find that the wave-like nature of bosonic stars has a large impact on the gravitational-wave emission. In particular, we show that the initial relative phase $\Delta \epsilon =\epsilon_1-\epsilon_2$ of the two complex fields forming the stars (or equivalently, the relative phase at merger) strongly impacts both the emitted gravitational-wave energy and the corresponding mode structure. This leads to a non-monotonic dependence of the emission on the frequency of the secondary star $\omega_2$, for fixed frequency $\omega_1$ of the primary. This phenomenology, which has not been found for the case of black-hole mergers, reflects the distinct ability of the Proca field to interact with itself in both constructive and destructive manners. We postulate this may serve as a smoking gun to shed light on the possible existence of these objects., Comment: Updated version

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 non-linear 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 non-ultracompact configurations or collapse to BHs. In concrete examples we show that typical migration/collapse time scales are not larger than $\sim 10^3$ 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., Comment: 5 pages + Appendices; Videos can be found in this URL http://gravitation.web.ua.pt/node/3889; v2. Title changed per request of journal. Published in Physical Review Letters as Editor's Suggestion and Featured in Physics

A mechanism for circumventing the Mayo-Bekenstein no-hair theorem allows endowing four dimensional $(D=4)$ asymptotically flat, spherical, electro-vacuum black holes with a minimally coupled $U(1)$-gauged scalar field profile: $Q$-$hair$. The scalar field must be massive, self-interacting and obey a {\it resonance condition} at the threshold of (charged) superradiance. We establish generality for this mechanism by endowing three different types of static black objects with scalar hair, within a $D=5$ Einstein-Maxwell-gauged scalar field model: asymptotically flat black holes and black rings; and black strings which asymptote to a Kaluza-Klein vacuum. These $D=5$ $Q$-hairy black objects share many of the features of their $D=4$ counterparts. In particular, the scalar field is subject to a resonance condition and possesses a $Q$-ball type potential. For the static black ring, the charged scalar hair can balance it, yielding solutions that are singularity free on and outside the horizon., Comment: 30 pages, 8 figures

The local thermodynamic stability of a black hole (BH) in the canonical ensemble is defined by the positivity of the specific heat at constant global charges. Schwarzschild BHs in thermodynamic equilibrium with an energy reservoir are always unstable against small fluctuations of energy, whereas sufficiently near-extremal Reissner-Nordstr\"{o}m/Kerr BHs are stable. One could expect that asymptotically-flat hairy BHs branching off from such stable phases would also be, by continuity, locally thermodynamically stable for vanishingly little hair. We show this is not the case in some models, including scalarized BHs bifurcating from Reissner-Nordstr\"{o}m and spinning BHs with synchronized hair bifurcating from Kerr. Specifically, it is found that quasi-bald BHs are locally thermodynamically unstable in the canonical ensemble for all global charges and regardless of being dynamically and entropically preferred over bald ones at fixed global charges., Comment: 11 pages, 4 figures. Comments are welcome

Derrick-type virial identities, obtained via dilatation (scaling) arguments, have a variety of applications in field theories. We deconstruct such virial identities in relativistic gravity showing how they can be recast as self-evident integrals of appropriate combinations of the equations of motion. In spherical symmetry, the appropriate combination and gauge choice guarantee the geometric part can be integrated out to yield a master form of the virial identity as a non-trivial energy-momentum balance condition, valid for both asymptotically flat black holes and self-gravitating solitons, for any matter model. Specifying the matter model we recover previous results obtained via the scaling procedure. We then discuss the more general case of stationary, axi-symmetric, asymptotically flat black hole or solitonic solutions in General Relativity, for which a master form for their virial identity is proposed, in a specific gauge but regardless of the matter content. In the flat spacetime limit, the master virial identity for both the spherical and axial cases reduces to a balance condition for the principal pressures, discussed by Deser., Comment: 14 pages

We present the first systematic search for exotic compact mergers in Advanced LIGO and Virgo events. We compare the short gravitational-wave signals GW190521, GW190426$\_$190642, GW200220$\_$061928 and the trigger 200114$\_$020818 (or S200114f) to a new catalogue of 759 numerical simulations of head-on mergers of horizonless exotic compact objects known as Proca stars, interpreted as self-gravitating lumps of (fuzzy) dark matter sourced by an ultralight (vector) bosonic particle. The Proca-star merger hypothesis is strongly rejected with respect to the black hole merger one by GW190426, weakly rejected by GW200220 and weakly favoured by GW190521 and S200114f. GW190521 and GW200220 yield highly consistent boson masses of $\mu_{\rm B} = 8.69^{+0.61}_{-0.75}\times10^{-13}$ eV and $\mu_{\rm B} = 9.13^{+1.18}_{-1.30}\times10^{-13}$ eV at the $90\%$ credible level. We conduct a preliminary population study of the compact binaries behind these events. Excluding (including) S200114f as a real event, and ignoring boson-mass consistencies across events, we estimate a fraction of Proca-star mergers of $\zeta = 0.27^{+0.43}_{-0.25} \ (0.39^{+0.38}_{-0.33})$. We discuss the impact of boson-mass consistency across events in such estimates. Our results maintain GW190521 as a Proca-star merger candidate and pave the way towards population studies considering exotic compact objects., Comment: Version accepted in Phys.Rev.D. 27 pages, 16 Figures, 4 Appendixes

Detection and parameter inference of gravitational-wave signals \ncor{from compact mergers} rely on the comparison of the incoming detector strain data $d(t)$ to waveform templates for the gravitational-wave strain $h(t)$ that ultimately rely on the resolution of Einstein's equations via numerical relativity simulations. These, however, commonly output a quantity known as the Newman-Penrose scalar $\psi_4(t)$ which, under the Bondi gauge, is related to the gravitational-wave strain by $\psi_4(t)=\mathrm{d}^2h(t) / \mathrm{d}t^2$. Therefore, obtaining strain templates involves an integration process that introduces artefacts that need to be treated in a rather manual way. By taking second-order finite differences on the detector data and inferring the corresponding background noise distribution, we develop a framework to perform gravitational-wave data analysis directly using $\psi_4(t)$ templates. We first demonstrate this formalism, and the impact of integration artefacts in strain templates, through the recovery of numerically simulated signals from head-on collisions of Proca stars injected in Advanced LIGO noise. Next, we re-analyse the event GW190521 under the hypothesis of a Proca-star merger, obtaining results equivalent to those in Ref.[1], where we used the classical strain framework. We find, however, that integration errors would strongly impact our analysis if GW190521 was four times louder. Finally, we show that our framework fixes significant biases in the interpretation of the high-mass GW trigger S200114f arising from the usage of strain templates. We remove the need to obtain strain waveforms from numerical relativity simulations, avoiding the associated systematic errors., Comment: Version accepted for publication in Physical Review X. 27 pages, 11 Figures, 3 Appendixes

Because the Klein-Gordon and Proca equations involve $\hbar$, they describe quantum fields. Their solutions, however, may be treated as classical if their typical action obeys $S^{\rm typical}\gg \hbar$. This is possible due to their bosonic nature, allowing states with many particles. We show, by generic arguments, that the typical action for such bosonic stars is ${\mathcal{S}^{\rm typical}}/{\hbar}\gtrsim \left({M^{\rm max}}/{M_{\rm Pl}}\right)^2\sim 10^{76}\left({M^{\rm max}}/{M_\odot}\right)^2$, where $M^{\rm max}$ is the maximal bosonic star mass of the particular model and $M_{\rm Pl}$ is the Planck mass. Thus, for models allowing $M^{\rm max}\gg M_{\rm Pl}$ and for solutions with mass $\sim M^{\rm max}$, the classical treatment is legitimate, which includes masses in the astrophysical interesting range $\gtrsim M_\odot$., Comment: 11 pages; Essay written for the Gravity Research Foundation 2022 Awards for Essays on Gravitation and selected for Honorable Mention

We examine the constraining power of current gravitational-wave data on scalar-tensor-Gauss-Bonnet theories that allow for the spontaneous scalarization of black holes. In the fiducial model that we consider, a slowly rotating black hole must scalarize if its size is comparable to the new length scale $\lambda$ that the theory introduces, although rapidly rotating black holes of any mass are effectively indistinguishable from their counterparts in general relativity. With this in mind, we use the gravitational-wave event GW190814$\,\unicode{x2014}\,$whose primary black hole has a spin that is bounded to be small, and whose signal shows no evidence of a scalarized primary$\,\unicode{x2014}\,$to rule out a narrow region of the parameter space. In particular, we find that values of ${\lambda \in [56, 96]~M_\odot}$ are strongly disfavored with a Bayes factor of $0.1$ or less. We also include a second event, GW151226, in our analysis to illustrate what information can be extracted when the spins of both components are poorly measured., Comment: Version accepted for publication. 8 pages + references, 4 figures. Some minor clarifications added relative to v1

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' ($i.e.$ 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., Comment: 11 pages, 3 figures

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 \textit{vicinity of the horizon} the effect of the magnetic field $B$ on a black hole of mass $M$, up to $BM\lesssim 1$, works \textit{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., Comment: 8 pages, 2 figures

Current gravitational wave (GW) detections rely on the existence of libraries of theoretical waveforms. Consequently, finding new physics with GWs requires libraries of non-standard models, which are computationally demanding. We discuss how deep learning frameworks can be used to generate new waveforms "learned" from a simulation dataset obtained, say, from numerical relativity simulations. Concretely, we use the WaveGAN architecture of a generative adversarial network (GAN). As a proof of concept we provide this neural network (NN) with a sample of ($>500$) waveforms from the collisions of exotic compact objects (Proca stars), obtained from numerical relativity simulations. Dividing the sample into a training and a validation set, we show that after a sufficiently large number of training epochs the NN can produce from 12\% to 25\% of the synthetic waveforms with an overlapping match of at least 95\% with the ones from the validation set. We also demonstrate that a NN can be used to predict the overlapping match score, with 90\% of accuracy, of new synthetic samples. These are encouraging results for using GANs for data augmentation and interpolation in the context of GWs, to cover the full parameter space of, say, exotic compact binaries, without the need of intensive numerical relativity simulations., Comment: 20 pages, 13 figures, 4 tables

Scalar boson stars and Dirac stars are solitonic solutions of the Einstein{Klein-Gordon and Einstein- Dirac classical equations, respectively. Despite the different bosonic vs: fermionic nature of the matter field, these solutions to the classical field equations have been shown to have qualitatively similar features [1]. In particular, for spinning stars the most fundamental configurations can be in both cases toroidal, unlike spinning Proca stars that are spheroidal [2]. In this paper we gauge the scalar and Dirac fields, by minimally coupling them to standard electromagnetism. We explore the impact of the gauge coupling on the resulting solutions. One of the most relevant difference concerns the gyromagnetic ratio, which for the scalar stars takes values around 1, whereas for Dirac stars takes values around 2., Comment: 11 pages, 6 figures. Accepted in Phys. Lett. B

The general relativity vacuum black holes (BHs) can be scalarised in models where a scalar field non-minimally couples to the Gauss-Bonnet (GB) invariant. Such GB scalarisation comes in two flavours, depending on the GB sign that triggers the phenomenon. Hereafter these two cases are termed GB$^\pm$ scalarisation. For vacuum BHs, only GB$^+$ scalarisation is possible in the static case, while GB$^-$ scalarisation is $spin$ induced. But for electrovacuum BHs, GB$^-$ is also $charged$ induced. We discuss the GB$^-$ scalarisation of Reissner-Nordstr\"om and Kerr-Newman BHs, discussing zero modes and constructing fully non-linear solutions. Some comparisons with GB$^+$ scalarisation are given. To assess the generality of the observed features, we also briefly consider the GB$^\pm$ scalarisation of stringy dilatonic BHs and coloured BHs which provide qualitative differences with respect to the electrovacuum case., Comment: 16 pages, 6 figures

We consider a family of new Higgs-Chern-Simons (HCS) gravity models in 2n+1 dimensions (n=1,2,3). This provides a generalization of the (usual) gravitational Chern-Simons (CS) gravitaties resulting from non- Abelian CS densities in all odd dimensions, which feature vector and scalar fields in addition to the metric. The derivation of the new HCS gravitational (HCSG) actions follows the same method as in the usual-CSG case resulting from the usual CS densities. The HCSG result from the HCS densities, which result through a one-step descent of the Higgs-Chern-Pontryagin (HCP), the latter being descended from Chern-Pontryagin (CP) densities in some even dimension. A preliminary study of the solutions of these models is considered, with exact solutions being reported for spacetime dimensions d = 3, 5., Comment: 10 pages

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 $\epsilon$ 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, $\epsilon\lesssim 0.29$ (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 $\epsilon\lesssim 0.10$, 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., Comment: 11 pages, 4 figures, 2 tables. Comments are welcome

We study the time evolution of spherical, excited ($i.e.$ nodeful) boson star models. We consider a model including quartic self-interactions, controlled by a coupling $\Lambda$. Performing non-linear simulations of the Einstein-(complex)-Klein-Gordon system, using as initial data equilibrium boson stars solutions of that system, we assess the impact of $\Lambda$ in the stability properties of the boson stars. In the absence of self-interactions ($\Lambda=0$), we observe the known behaviour that the excited stars in the (candidate) stable branch decay to a non-excited star without a node; however, we show that for large enough values of the self-interactions coupling, these excited stars do not decay (up to timescales of about $t\sim 10^4$). The stabilization of the excited states for large enough self-interactions is further supported by evidence that the nodeful states dynamically form through the gravitational cooling mechanism, starting from dilute initial data. Our results support the healing power (against dynamical instabilities) of self-interactions, recently unveiled in the context of the non-axisymmetric instabilities of spinning boson stars., Comment: 14 pages

Virial (aka scaling) identities are integral identities that are useful for a variety of purposes in non-linear field theories, including establishing no-go theorems for solitonic and black hole solutions, as well as for checking the accuracy of numerical solutions. In this paper, we provide a pedagogical rationale for the derivation of such integral identities, starting from the standard variational treatment of particle mechanics. In the framework of one-dimensional (1D) effective actions, the treatment presented here yields a set of useful formulas for computing virial identities in any field theory. Then, we propose that a complete treatment of virial identities in relativistic gravity must take into account the appropriate boundary term. For General Relativity this is the Gibbons-Hawking-York boundary term. We test and confirm this proposal with concrete examples. Our analysis here is restricted to spherically symmetric configurations, which yield 1D effective actions (leaving higher-D effective actions and in particular the axially symmetric case to a companion paper). In this case, we show that there is a particular "gauge" choice, $i.e.$ a choice of coordinates and parameterizing metric functions, that simplifies the computation of virial identities in General Relativity, making both the Einstein-Hilbert action and the Gibbons-Hawking-York boundary term non-contributing. Under this choice, the virial identity results exclusively from the matter action. For generic "gauge" choices, however, this is not the case., Comment: 27 pages, 1 figure

We construct families, and concrete examples, of simple extensions of the Standard Model that can yield ultralight {real or} complex vectors or scalars with potential astrophysical relevance. Specifically, the mass range for these putative fundamental bosons ($\sim 10^{-10}-10^{-20}$ eV) would lead dynamically to both new non-black hole compact objects (bosonic stars) and new non-Kerr black holes, with masses of $\sim M_\odot$ to $\sim 10^{10} M_\odot$, corresponding to the mass range of astrophysical black hole candidates (from stellar mass to supermassive). For each model, we study the properties of the mass spectrum and interactions after spontaneous symmetry breaking, discuss its theoretical viability and caveats, as well as some of its potential and most relevant phenomenological implications {linking them to the} physics of compact objects., Comment: 27 pages, 2 figures