According to the no-hair theorem, astrophysical black holes are uniquely characterized by their masses and spins and are described by the Kerr metric. Several parametric deviations from the Kerr metric have been suggested to study observational signatures in both the electromagnetic and gravitational-wave spectra that differ from the expected Kerr signals. Due to the no-hair theorem, however, such spacetimes cannot be regular everywhere outside the event horizons, if they are solutions to the Einstein field equations; they are often characterized by naked singularities or closed time-like loops in the regions of the spacetime that are accessible to an external observer. For observational tests of the no-hair theorem that involve phenomena in the vicinity of the circular photon orbit or the innermost stable circular orbit around a black hole, these pathologies limit the applicability of the metrics only to compact objects that do not spin rapidly. In this paper, we construct a Kerr-like metric which depends on a set of free parameters in addition to its mass and spin and which is regular everywhere outside of the event horizon. We derive expressions for the energy and angular momentum of a particle on a circular equatorial orbit around the black hole and compute the locations of the innermost stable circular orbit and the circular photon orbit. We demonstrate that these orbits change significantly for even moderate deviations from the Kerr metric. The properties of our metric make it an ideally suited spacetime to carry out strong-field tests of the no-hair theorem in the electromagnetic spectrum using the properties of accretion flows around astrophysical black holes of arbitrary spin.
One avenue for testing the no-hair theorem is obtained through timing a pulsar orbiting close to a black hole and fitting for quadrupolar effects on the time-of-arrival of pulses. If deviations from the Kerr quadrupole are measured, then the no-hair theorem is invalidated. To this end, we derive an expression for the light travel time delay for a pulsar orbiting in a black-hole spacetime described by the Butterworth-Ipser metric, which has an arbitrary spin and quadrupole moment. We consider terms up to the quadrupole order in the black-hole metric and derive the time-delay expression in a clo…
The spinning-hairy black holes that occur in Einstein gravity supplemented by a doublet of complex scalar fields are constructed within an extension of the model by a $U(1)$ gauge symmetry involving a massless vector potential. The hairy black holes then acquire an electric charge and a magnetic moment; their domain of existence is discussed in terms of the gauge coupling constant.
It has recently been revealed that spinning black holes of the photon-fluid model can support acoustic `clouds', stationary density fluctuations whose spatially regular radial eigenfunctions are determined by the $(2+1)$-dimensional Klein-Gordon equation of an effective massive scalar field. Motivated by this intriguing observation, we use {\it analytical} techniques in order to prove a no-short hair theorem for the composed acoustic-black-hole-scalar-clouds configurations. In particular, it is proved that the effective lengths of the stationary bound-state co-rotating acoustic scalar clouds a…
We obtain spinning boson star solutions and hairy black holes with synchronised hair in the Einstein-Klein-Gordon model, wherein the scalar field is massive, complex and with a non-minimal coupling to the Ricci scalar. The existence of these hairy black holes in this model provides yet another manifestation of the universality of the synchronisation 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, qualitative…
Self-interacting boson stars have been shown to alleviate the astrophysically low maximal mass of their non-self-interacting counterparts. We report some physical features of spinning self-interacting boson stars, namely their compactness, the occurence of ergo-regions and the scalar field profiles, for a sample of values of the coupling parameter. The results agree with the general picture that these boson stars are comparatively less compact than the non-self-interacting ones. We also briefly discuss the effect of scalar self-interactions on the properties of Kerr black holes with scalar hai…
Two asymptotically flat spinning black holes balanced by their self-interacting, synchronised scalar hair
Universidade de Aveiro（阿威罗大学）；Centre for Research and Development in Mathematics and Applications (CIDMA)（数学与应用研究中心）；Universidade Federal do Pará（帕拉联邦大学）
We consider the $\mathrm{O}(3)$ non-linear sigma-model, composed of three real scalar fields with a standard kinetic term and with a symmetry breaking potential in four spacetime dimensions. We show that this simple, geometrically motivated model, admits both self-gravitating, asymptotically flat, non-topological solitons and hairy black holes, when minimally coupled to Einstein's gravity, $without$ the need to introduce higher order kinetic terms in the scalar fields action. Both spherically symmetric and spinning, axially symmetric solutions are studied. The solutions are obtained under a an…
Recent studies have made key progress on the black hole/solitonic solutions of the Einstein-Proca system. Firstly, fully non-linear dynamical evolutions of the Kerr black hole superradiant instability, triggered by a Proca field, have shown the formation of a new equilibrium state, a spinning black hole with synchronised Proca hair. Secondly, non-linear evolutions of spinning Proca stars have established that they are dynamically stable, unlike their scalar cousins. Thirdy, separability of the Proca equation on the Kerr background has been achieved. Motivated by these results, in this paper we…
We construct rotating boson stars and Myers-Perry black holes with scalar hair (MPBHsSH) as fully non-linear solutions of five dimensional Einstein gravity minimally coupled to a complex, massive scalar field. The MPBHsSH are, in general, regular on and outside the horizon, asymptotically flat, and possess angular momentum in a single rotation plane. They are supported by rotation and have no static limit. Such hairy BHs may be thought of as bound states of boson stars and singly spinning, vacuum MPBHs and inherit properties of both these building blocks. When the horizon area shrinks to zero,…
We study solutions of the Einstein-Skyrme model. Firstly we consider test field Skyrmions on the Kerr background. These configurations -- hereafter dubbed Skerrmions -- can be in equilibrium with a Kerr black hole (BH) by virtue of a synchronisation condition. We consider two sectors for Skerrmions. In the sector with non-zero baryon charge, Skerrmions are akin to the known Skyrme solutions on the Schwarzschild background. These `topological' configurations reduce to flat spacetime Skyrmions in a vanishing BH mass limit; moreoever, they never become "small" perturbations on the Kerr background…
The Einstein-Gauss-Bonnet gravity in five dimensions is extended by scalar fields and the corresponding equations are reduced to a system of non-linear differential equations. A large family of regular solutions of these equations is shown to exist. Generically, these solutions are spinning black holes with scalar hairs. They can be characterized (but not uniquely) by an horizon and an angular velocity on this horizon. Taking particular limits the black holes approach boson star or become extremal, in any case the limiting configurations remain hairy.
The last years have brought upon us a golden age of observational gravitational physics. The several observations by the LIGO/Virgo/KAGRA collaboration about gravitational waves and by the EHT collaboration about the shadow and lensing of light around the supermassive black hole in the centre of M87 will point the scientific community in the correct direction to find an answer to the Kerr hypothesis. In order to follow that direction, the systematic construction and analysis of the physical properties of solutions within General Relativity with additional fields or within modified theories of …
Recent work paints a conflicting portrait of the distribution of black hole spins in merging binaries measured with gravitational waves. Some analyses find that a significant fraction of merging binaries contain at least one black hole with a spin tilt $>90^\circ$ with respect to the orbital angular momentum vector, which has been interpreted as a signature for dynamical assembly. Other analyses find the data are consistent with a bimodal population in which some binaries contain black holes with negligible spin while the rest contain black holes with spin vectors preferentially aligned with t…
We perform general relativistic simulations of self-gravitating black hole-disks in which the spin of the black hole is significantly tilted ($45^\circ$ and $90^\circ$) with respect to the angular momentum of the disk and the disk-to-black hole mass ratio is $16\%-28\%$. The black holes are rapidly spinning with dimensionless spins up to $\sim 0.97$. These are the first self-consistent hydrodynamic simulations of such systems, which can be prime sources for multimessenger astronomy. In particular tilted black hole-disk systems lead to: i) black hole precession; ii) disk precession and warping …
This is a brief summary of the most important hairy black hole solutions in 3+1 spacetime dimensions discovered over the last 25 years. These were first of all the Einstein-Yang-Mills black holes and their various generalizations including the Higgs field, the dilaton and the curvature corrections, and also the Skyrme black holes. More recently, these were black holes supporting a scalar field violating the energy conditions or non-minimally coupled to gravity, and also spinning black holes with massive complex scalar hair. Finally, these were black holes with massive graviton hair.
We study Kerr black holes with synchronised non-trivial parity-odd massive scalar hair in four dimensional asymptotically flat space-time. These axially symmetric stationary spinning solutions of the minimally coupled Einstein-Klein-Gordon theory provide yet another example of bound states in synchronous rotation with the event horizon. We discuss the properties of these parity-odd hairy black holes and boson stars and exhibit their domain of existence. Considering the ergo-regions of these hairy black holes, we show that apart from the previously discussed ergo-sphere and ergo-Saturn, they su…
Recently, various examples of asymptotically flat, rotating black holes (BHs) with synchronized hair have been explicitly constructed, including Kerr BHs with scalar or Proca hair, and Myers-Perry BHs with scalar hair and a mass gap, showing there is a general mechanism at work. All these solutions have been found numerically, integrating the fully non-linear field equations of motion from the event horizon outwards. Here, we address the spacetime geometry of these solutions inside the event horizon. Firstly, we provide arguments, within linear theory, that there is no regular inner horizon fo…
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 …
It has recently been proved numerically that spinning black holes in Einstein-scalar theories which are characterized by a non-minimal negative coupling of the scalar field to the Gauss-Bonnet invariant of the curved spacetime may develop exponentially growing instabilities. Intriguingly, it has been demonstrated that this tachyonic instability, which marks the onset of the spontaneous scalarization phenomenon in the Einstein-Gauss-Bonnet-scalar theory, characterizes spinning black holes whose dimensionless angular momentum parameter ${\bar a}\equiv a/M$ is larger than some critical value ${\b…
We compute the radiation emitted by a particle on the innermost stable circular orbit of a rapidly spinning black hole both (a) analytically, working to leading order in the deviation from extremality and (b) numerically, with a new high-precision Teukolsky code. We find excellent agreement between the two methods. We confirm previous estimates of the overall scaling of the power radiated, but show that there are also small oscillations all the way to extremality. Furthermore, we reveal an intricate mode-by-mode structure in the flux to infinity, with only certain modes having the dominant sca…
The ability of a plasma surrounding spinning black holes to extract rotational energy and power energetic emissions has been recognized as a key astrophysical phenomenon. Important insights into the nature of this process are obtained through the analysis of the interplay between a force-free magnetosphere and the black hole. This task involves solving a complicated system of equations, often requiring complex numerical simulations. Recent analytical attempts at tackling this problem have exploited the fact that the near horizon region of extreme Kerr (NHEK) is endowed with an enhanced symmetr…
Ringdown of a postinnermost stable circular orbit of a rapidly spinning black hole: Mass ratio dependence of higher harmonic quasinormal mode excitation
The universal relaxation bound suggests that the relaxation times of perturbed thermodynamical systems is bounded from below by the simple time-times-temperature (TTT) quantum relation $τ\times T\geq {{\hbar}\overπ}$. It is known that some perturbation modes of near-extremal Kerr black holes in the regime $MT_{\text{BH}}/\hbar\ll m^{-2}$ are characterized by normalized relaxation times $πτ\times T_{\text{BH}}/\hbar$ which, in the approach to the limit $MT_{\text{BH}}/\hbar\to0$, make infinitely many oscillations with a tiny constant amplitude around $1$ and therefore cannot be used directly to…
Some quantum-gravity theories suggest that the absorbing horizon of a classical black hole should be replaced by a reflective surface which is located a microscopic distance above the would-be classical horizon. Instead of an absorbing black hole, the resulting horizonless spacetime describes a reflective exotic compact object. Motivated by this intriguing prediction, in the present paper we explore the physical properties of exotic compact objects which are linearly coupled to stationary bound-state massive scalar field configurations. In particular, solving the Klein-Gordon wave equation for…
The LIGO-Virgo collaboration recently reported the properties of GW190412, a binary black hole merger with unequal component masses (mass ratio $0.25^{+0.06}_{-0.04}$ when using the EOBNR PHM approximant) and a non-vanishing effective spin aligned with the orbital angular momentum. They used uninformative priors to infer that the more massive black hole had a dimensionless spin magnitude between 0.17 and 0.59 at 90\% confidence. We argue that, within the context of isolated binary evolution, it is more natural to assume a priori that the first-born, more massive black hole has a negligible spi…
The spins of a number of supermassive and stellar-mass black holes have been measured based on detections of thermal continuum emission and relativistically broadened iron lines in their x-ray spectra. Likewise, quasiperiodic variability has been observed in several sources. Such measurements commonly make the assumption that black holes are described by the Kerr metric, which according to the no-hair theorem characterizes black holes uniquely in terms of their masses and spins. This fundamental property of black holes can be tested observationally by measuring potential deviations from the Ke…
We study rapidly spinning compact stars with equations of state featuring a first order phase transition between strongly coupled nuclear matter and deconfined quark matter by employing the gauge/gravity duality. We consider a family of models, which allow purely hadronic uniformly rotating stars with masses up to approximately $2.9\, \mathrm{M}_\odot$, and are therefore compatible with the interpretation that the secondary component ($2.59^{+0.08}_{-0.09}\, \mathrm{M}_\odot$) in GW190814 is a neutron star. These stars have central densities several times the nuclear saturation density so that…
The recent detection of gravitational waves by the LIGO/VIRGO collaboration has allowed for the first tests of Einstein's theory in the extreme gravity regime, where the gravitational interaction is simultaneously strong, non-linear and dynamical. One such test concerns the rate at which the binaries inspiral, or equivalently the rate at which the gravitational wave frequency increases, which can constrain the existence of hairy black holes. This is because black holes with scalar hair typically excite dipole radiation, which in turn leads to a faster decay rate and frequency chirping. In this…
We study a new family of self-gravitating axially-symmetric, rotating boson stars in the two-component Friedberg-Lee-Sirlin model minimally coupled to Einstein gravity in four spacetime dimensions. In the flat space limit the 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…
We revisit the problem of a spinning black hole immersed in a uniformly magnetized plasma within the context of force-free electrodynamics. Such configurations have been found to relax to stationary jetlike solutions that are powered by the rotational energy of the black hole. We write down an analytic description for the jet solutions in the low black hole spin limit, and demonstrate that it provides a good approximation to the configurations found dynamically. For characterizing the magnetospheres of rapidly spinning black holes, we find that the current sheet which forms in the black hole e…
The opportunity to study physics at supra-nuclear densities through X-ray observations of neutron stars has led to in-depth investigations of certain approximately universal relations that can remove degeneracies in pulse profile models. One such set of relations determines all of the multipole moments of a neutron star just from the first three (the mass monopole, the current dipole and the mass quadrupole moment) approximately independently of the equation of state. These three-hair relations were found to hold in neutron stars that rotate rigidly, as is the case in old pulsars, but neutron …
The recent detection of GW190814 featured the merger of a binary with a primary having a mass of $\sim 23\,M_{\odot}$ and a secondary with a mass of $\sim 2.6\,M_{\odot}$. While the primary was most likely a black hole, the secondary could be interpreted as either the lightest black hole or the most massive neutron star ever observed, but also as the indication of a novel class of exotic compact objects. We here argue that the secondary in GW190814 needs not be an ab-initio black hole nor an exotic object; rather, based on our current understanding of the nuclear-matter equation of state, it c…
We obtain a novel exact analytical solution to Einstein-Maxwell-scalar gravity with negative cosmological constant in (2+1)-dimensions. The scalar field is minimally coupled to gravity and electromagnetism by the metric ansatz. On the one hand, we first find analytical results for the real part of quasinormal mode spectrum of a rotating hairy Bañados-Teitelboim-Zanelli (BTZ) black hole by solving the associated Dirac equation through the pseudo-Hermitian quantum mechanical tools within the framework of discrete-basis-set method. We then show that, in the spinless case, these quasinormal modes …
Light bosonic fields are ubiquitous in extensions of the Standard Model. Even when minimally coupled to gravity, these fields might evade the assumptions of the black-hole no-hair theorems and give rise to spinning black holes which can be drastically different from the Kerr metric. Furthermore, they allow for self-gravitating compact solitons, known as (scalar or Proca) boson stars. The quasi-periodic oscillations (QPOs) observed in the X-ray flux emitted by accreting compact objects carry information about the strong-field region, thus providing a powerful tool to constrain deviations from K…
