No-hair Research Articles

The gravimagnetic dipole

We investigate a previously constructed stationary solution of the vacuum Einstein equations, which represents a system of two non-extreme black holes with equal masses and opposite NUT charges, connected by a Misner string with tension. For large separations, the inverse square law force measured by this tension is attractive or repulsive, according to the relative values of the masses and NUT charges. For small separations, the force is always repulsive, so that the system cannot collapse to a single black hole. For given values of the black hole masses and NUT charges, there is a unique configuration such that the Misner string is tensionless. This behaves asymptotically as the Kerr solution, but can be overspinning while remaining free from a ring singularity, thus evading the usual black hole uniqueness theorems. All double black hole and string configurations satisfy a generalized first law of black hole mechanics where the two black holes and the Misner string are treated on an equal footing.

Gravitational lensing by hairy black holes in Einstein-scalar-Gauss-Bonnet theories

We investigate the weak and strong deflection gravitational lensing by the hairy black holes in the Einstein-scalar-Gauss-Bonnet (EsGB) gravity with five types of coupling functions (quadratic, cubic, quartic, inverse-polynomial, and logarithmic), which can evade the no-hair theorem. The lensing observables are found and the possibility of detecting the effects of the scalar hair is analyzed. We find that all of the shadows cast by these black holes are consistent with the measurement by the Event Horizon Telescope, while other lensing observables are beyond the present capacity. Therefore, it is currently impossible to distinguish these black holes from the Schwarzschild one and from each other merely by their lensing signatures, leaving testing the EsGB gravity by gravitational lensing until new technology is available.

Lessons from black hole quasinormal modes in modified gravity

Quasinormal modes (QNMs) of perturbed black holes have recently gained much interest because of their tight relations with the gravitational wave signals emitted during the post-merger phase of a binary black hole coalescence. One of the intriguing features of these modes is that they respect the no-hair theorem, and hence, they can be used to test black hole spacetimes and the underlying gravitational theory. In this paper, we exhibit three different aspects of how black hole QNMs could be altered in theories beyond Einstein’s general relativity (GR). These aspects are (i) the direct alterations of QNM spectra as compared with those in GR, (ii) the violation of the geometric correspondence between the high-frequency QNMs and the photon geodesics around the black hole, and (iii) the breaking of the isospectrality between the axial and polar gravitational perturbations. Several examples will be provided in each individual case. The prospects and possible challenges associated with future observations will be also discussed.

Spontaneous vectorization of electrically charged black holes

In this work, we generalize the spontaneous scalarization phenomena in Einstein-Maxwell-scalar models to a higher spin field. The result is an Einstein-Maxwell-vector model wherein a vector field is nonminimally coupled to the Maxwell invariant by an exponential coupling function. We show that the latter guarantees the circumvention of an associated no-hair theorem when the vector field has the form of an electric field. Different than its scalar counterpart, the new spontaneously vectorized Reissner-Nordstr\"om (RN) black holes are, always, undercharged while being entropically preferable. The solution profile and domain of existence are presented and analyzed.

Extending the Frequency Reach of Pulsar Timing Array-based Gravitational Wave Search without High-cadence Observations

Abstract Gravitational wave (GW) searches using pulsar timing arrays (PTAs) are assumed to be limited by the typical average observational cadence of 1/(2 weeks) for a single pulsar to GW frequencies ≲4 × 10−7 Hz. We show that this assumption is incorrect and that a PTA can detect signals with much higher frequencies, which are preserved in the data due to aliasing, by exploiting asynchronous observations from multiple pulsars. This allows an observation strategy that is scalable to future large-scale PTAs containing O(103) pulsars, enabled by the Five-hundred meter Aperture Spherical Telescope and the Square Kilometer Array, without requiring a higher per-pulsar observation cadence. We show that higher frequency GW observations, reaching up to 4 × 10−4 Hz with an Square Kilometer Array-era PTA, have significant astrophysical implications, such as (i) a three orders of magnitude better constraint than current high-cadence observations on GW strain in the [10, 400] μHz band, and (ii) sensitive tests of the no-hair theorem in the mass range of supermassive black hole binaries using their inspiral, merger, and ringdown signals.

Black-hole spectroscopy, the no-hair theorem, and GW150914: Kerr versus Occam

The "no-hair" theorem states that astrophysical black holes are fully characterised by just two numbers: their mass and spin. The gravitational-wave emission from a perturbed black-hole consists of a superposition of damped sinusoids, known as \textit{quasi-normal modes}. Quasi-normal modes are specified by three integers $(\ell,m,n)$: the $(\ell, m)$ integers describe the angular properties and $(n)$ specifies the (over)tone. If the no-hair theorem holds, the frequencies and damping times of quasi-normal modes are determined uniquely by the mass and spin of the black hole, while phases and amplitudes depend on the particular perturbation. Current tests of the no-hair theorem, attempt to identify these modes in a semi-agnostic way, without imposing priors on the source of the perturbation. This is usually known as \textit{black-hole spectroscopy}. Applying this framework to GW150914, the measurement of the first overtone led to the confirmation of the theorem to $20\%$ level. We show, however, that such semi-agnostic tests cannot provide strong evidence in favour of the no-hair theorem, even for extremely loud signals, given the increasing number of overtones (and free parameters) needed to fit the data. This can be solved by imposing prior assumptions on the origin of the perturbed black hole that can further constrain the explored parameters: in particular, our knowledge that the ringdown is sourced by a binary black hole merger. Applying this strategy to GW150914 we find a natural log Bayes factor of $\sim 6.5$ in favour of the Kerr nature of its remnant, indicating that the hairy object hypothesis is disfavoured with $<1:600$ with respect to the Kerr black-hole one.

Stable small spatial hairs in a power-law k-inflation model

In this paper, we extend our investigation of the validity of the cosmic no-hair conjecture within non-canonical anisotropic inflation. As a result, we are able to figure out an exact Bianchi type I solution to a power-law k-inflation model in the presence of unusual coupling between scalar and electromagnetic fields as -f^2(phi )F_{mu nu }F^{mu nu }/4. Furthermore, stability analysis based on the dynamical system method indicates that the obtained solution does admit stable and attractive hairs during an inflationary phase and therefore violates the cosmic no-hair conjecture. Finally, we show that the corresponding tensor-to-scalar ratio of this model turns out to be highly consistent with the observational data of the Planck 2018.

Hairy black holes by gravitational decoupling

Black holes with hair represented by generic fields surrounding the central source of the vacuum Schwarzschild metric are examined under the minimal set of requirements consisting of i) the existence of a well defined event horizon and ii) the strong or dominant energy condition for the hair outside the horizon. We develop our analysis by means of the gravitational decoupling approach. We find that trivial deformations of the seed Schwarzschild vacuum preserve the energy conditions and provide a new mechanism to evade the no-hair theorem based on a primary hair associated with the charge generating these transformations. Under the above conditions i) and ii), this charge consistently increases the entropy from the minimum value given by the Schwarzschild geometry. As a direct application, we find a non-trivial extension of the Reissner-Nordstrom black hole showing a surprisingly simple horizon. Finally, the non-linear electrodynamics generating this new solution is fully specified.

No-hair theorems for noncanonical self-gravitating static multiple scalar fields

We prove under certain assumptions no-hair theorems for non-canonical self-gravitating static multiple scalar fields in spherically symmetric spacetimes. It is shown that the only static, spherically symmetric and asymptotically flat black hole solutions consist of the Schwarzschild metric and a constant multi-scalar map. We also prove that there are no static, horizonless, asymptotically flat, spherically symmetric solutions with static scalar fields and a regular center. The last theorem shows that the static, asymptotically flat, spherically symmetric reflecting compact objects with Neumann boundary conditions can not support a non-trivial self-gravitating non-canonical (and canonical) multi-scalar map in their exterior spacetime regions. In order to prove the no-hair theorems we derive a new divergence identity.

Infinitely degenerate exact Ricci-flat solutions in f(R) gravity

We obtain an infinite number of exact static, Ricci-flat spherically symmetric vacuum solutions for a class of f(R) theories of gravity. We analytically derive two exact vacuum black-hole solutions for the same class of f(R) theories. The two black-hole solutions have the event-horizon at the same point; however, their asymptotic features are different. Our results suggest that no-hair theorem may not hold for generic modified gravity theories. We discuss the implications of our work to distinguish modified gravity theories from general relativity in gravitational wave detections.

The Weak Cosmic Censorship Conjecture May Be Violated

According to traditional theory, the Schwarzschild black hole does not produce super-radiation. If the boundary conditions are set up in advance, this possibility will be combined with the boson-coupled wave function in the Schwarzschild black hole, where the incident boson will have a mirrored mass, so even the Schwarzschild black hole can generate super-radiation phenomena.Recently, an article of mine obtained interesting results about the Schwarzschild black hole can generate super-radiation phenomena. The result contains some conclusions that violate the no-hair theorem. We know that the phenomenon of black hole super-radiation is a process of entropy reduction I found that the weak cosmic censorship conjecture may be violated.

Detecting Scalar Fields with Extreme Mass Ratio Inspirals.

We study extreme mass ratio inspirals (EMRIs), during which a small body spirals into a supermassive black hole, in gravity theories with additional scalar fields. We first argue that no-hair theorems and the properties of known theories that manage to circumvent them introduce a drastic simplification to the problem: the effects of the scalar on supermassive black holes, if any, are mostly negligible for EMRIs in vast classes of theories. We then exploit this simplification to model the inspiral perturbatively and we demonstrate that the scalar charge of the small body leaves a significant imprint on gravitational wave emission. Although much higher precision is needed for waveform modeling, our results strongly suggest that this imprint is observable with Laser Interferometer Space Antenna, rendering EMRIs promising probes of scalar fields.

Thermal order in conformal theories

It is widely expected that at sufficiently high temperatures order is always lost, e.g. magnets loose their ferromagnetic properties. We pose the question of whether this is always the case in the context of quantum field theory in $d$ space dimensions. More concretely, one can ask whether there exist critical points (CFTs) which break some global symmetry at arbitrary finite temperature. The most familiar CFTs do not exhibit symmetry breaking at finite temperature, and moreover, in the context of the AdS/CFT correspondence, critical points at finite temperature are described by an uncharged black brane which obeys a no-hair theorem. Yet, we show that there exist CFTs which have some of their internal symmetries broken at arbitrary finite temperature. Our main example is a vector model which we study both in the epsilon expansion and arbitrary rank as well as the large rank limit (and arbitrary dimension). The large rank limit of the vector model displays a conformal manifold, a moduli space of vacua, and a deformed moduli space of vacua at finite temperature. The appropriate Nambu-Goldstone bosons including the dilaton-like particle are identified. Using these tools we establish symmetry breaking at finite temperature for finite small $\epsilon$. We also prove that a large class of other fixed points, which describe some of the most common quantum magnets, indeed behave as expected and do not break any global symmetry at finite temperature. We discuss some of the consequences of finite temperature symmetry breaking for the spectrum of local operators. Finally, we propose a class of fixed points which appear to be possible candidates for finite temperature symmetry breaking in $d=2$.

Science with the TianQin observatory: Preliminary result on extreme-mass-ratio inspirals

Systems consisting of a massive black hole and a stellar-origin compact object (CO), known as extreme-mass-ratio inspirals (EMRIs), are of great significance for space-based gravitational-wave detectors, as they will allow for testing gravitational theories in the strong field regime, and for checking the validity of the black hole no-hair theorem. In this work, we present a calculation of the EMRI rate and parameter estimation capabilities of the TianQin observatory, for various astrophysical models for these sources. We find that TianQin can observe EMRIs involving COs with mass of 10$M_\odot$ up to redshift $\sim2$. We also find that detections could reach tens or hundreds per year in the most optimistic astrophysical scenarios. Intrinsic parameters are expected to be recovered to within fractional errors of $\sim 10^{-6}$, while typical errors on the luminosity distance and sky localization are 10% and 10 deg$^2$, respectively. TianQin observation of EMRIs can also constrain possible deviations from the Kerr quadrupole moment to within fractional errors $\lesssim10^{-4}$. We also find that a network of multiple detectors would allow for improvements in both detection rates (by a factor $\sim 1.5$ -$3$) and in parameter estimation precision (20-fold improvement for the sky localization and fivefold improvement for the other parameters).

Spherically Symmetric Scalar Hair for Charged Black Holes.

The no-hair theorem by Mayo and Bekenstein states that there exists no nonextremal static and spherical charged black hole endowed with hair in the form of a charged scalar field with a self-interaction potential. In our recent work [Phys. Lett. B 803, 135324 (2020)PYLBAJ0370-2693], we showed that the effect of a scalar mass term is important at an asymptotic infinity, which was omitted to prove the no-hair theorem. In this Letter, we demonstrate that there actually exists static and spherical charged scalar hair, dubbed as Q hair, around charged black holes, by taking into account the backreaction to the metric and gauge field. We also discuss that Q cloud, which is constructed without the backreaction around a Reissner-Nordström black hole, is a good approximation to Q hair under a certain limit.

Black holes with scalar hair in light of the Event Horizon Telescope

Searching for violations of the no-hair theorem (NHT) is a powerful way to test gravity, and more generally fundamental physics, particularly with regards to the existence of additional scalar fields. The first observation of a black hole (BH) shadow by the Event Horizon Telescope (EHT) has opened a new direct window onto tests of gravity in the strong-field regime, including probes of violations of the NHT. We consider two scenarios described by the Einstein-Maxwell equations of General Relativity and electromagnetism, to which we add a scalar field. In the first case we consider a minimally-coupled scalar field with a potential, whereas in the second case the field is conformally-coupled to curvature. In both scenarios we construct charged BH solutions, which are found to carry primary scalar hair. We then compute the shadows cast by these two BHs as a function of their electric charge and scalar hair parameter. Comparing these shadows to the shadow of M87* recently imaged by the EHT collaboration, we set constraints on the amount of scalar hair carried by these two BHs. The conformally-coupled case admits a regime for the hair parameter, compatible with EHT constraints, describing a so-called mutated Reissner-Nordström BH: this solution was recently found to effectively mimic a wormhole. Our work provides novel constraints on fundamental physics, and in particular on violations of the no-hair theorem and the existence of additional scalar fields, from the shadow of M87*.

Spectroscopy of binary black hole ringdown using overtones and angular modes

The black hole uniqueness and the no-hair theorems imply that the quasinormal spectrum of any astrophysical black hole is determined solely by its mass and spin. The countably infinite number of quasinormal modes of a Kerr black hole are thus related to each other and any deviations from these relations provide a strong hint for physics beyond the general theory of relativity. To test the no-hair theorem using ringdown signals, it is necessary to detect at least two quasinormal modes. In particular, one can detect the fundamental mode along with a subdominant overtone or with another angular mode, depending on the mass ratio and the spins of the progenitor binary. Also in the light of the recent discovery of GW190412, studying how the mass ratio affects the prospect of black hole spectroscopy using overtones or angular modes is pertinent, and this is the major focus of our study. First, we provide ready-to-use fits for the amplitudes and phases of both the angular modes and overtones as a function of mass ratio $q\in[0,10]$. Using these fits we estimate the minimum signal-to-noise ratio for detectability, resolvability, and measurability of subdominant modes/tones. We find that performing black-hole spectroscopy with angular modes is preferable when the binary mass ratio is larger than $q\approx 1.2$ (provided that the source is not located at a particularly disfavoured inclination angle). For nonspinning, equal-mass binary black holes, the overtones seem to be the only viable option to perform a spectroscopy test of the no-hair theorem. However this would require a large ringdown signal-to-noise ratio ($\approx 100$ for a $5\%$ accuracy test with two overtones) and the inclusion of more than one overtone to reduce modelling errors, making black-hole spectroscopy with overtones impractical in the near future.

Electric multipole fields of higher-dimensional massive bodies

It was shown in a recent paper [J. Math. Phys. 60, 102502 (2019)] that slowly lowering an electric charge into a Schwarzschild-Tangherlini (ST) black hole endows the final state with electric multipole fields, which implies the final state geometry is not Reissner-Nordstr\"om-Tangherlini in nature. This conclusion departs from the four-dimensional case in which the no-hair theorem (NHT) requires the final state to be a Reissner-Nordstr\"om black hole. To better understand this discrepancy clearly requires a deeper understanding of the origin of the multipole hair in the higher-dimensional case. In this paper, we advance the conjecture that charged, static, and asymptotically-flat higher-dimensional black holes can acquire electric multipole hair only after they form. This supposition derives from studying the asymptotic behavior of the field of a multipole charge onto which a massive and hyperspherical shell with an exterior ST geometry is collapsing. In the mathematical limit as the shell approaches its ST radius, we find that the multipole fields (except the monopole) vanish. This implies that the only information of an arbitrary (but finite) charge distribution inside the collapsing shell that is available to an asymptotic observer is the total electric charge. Our results yield considerable insight into how higher-dimensional black holes acquire electric multipole hair, and also imply that, in four dimensions, the fadeaway of multipole moments during gravitational collapse is not strictly because of the NHT.

Hairy black-holes in shift-symmetric theories

Scalar hair of black holes in theories with a shift symmetry are constrained by the no-hair theorem of Hui and Nicolis, assuming spherical symmetry, time-independence of the scalar field and asymptotic flatness. The most studied counterexample is a linear coupling of the scalar with the Gauss-Bonnet invariant. However, in this case the norm of the shift-symmetry current J2 diverges at the horizon casting doubts on whether the solution is physically sound. We show that this is not an issue since J2 is not a scalar quantity, since Jμ is not a diffinvariant current in the presence of Gauss-Bonnet. The same theory can be written in Horndeski form with a non-analytic function G5∼ log X . In this case the shift-symmetry current is diff-invariant, but contains powers of X in the denominator, so that its divergence at the horizon is again immaterial. We confirm that other hairy solutions in the presence of non-analytic Horndeski functions are pathological, featuring divergences of physical quantities as soon as one departs from time-independence and spherical symmetry. We generalise the no-hair theorem to Beyond Horndeski and DHOST theories, showing that the coupling with Gauss-Bonnet is necessary to have hair.

Detectability of the subdominant mode in a binary black hole ringdown

The ringdown is the late part of the post-merger signature emitted during the coalescence of two black holes and comprises of a superposition of quasi-normal-modes. Within general relativity, because of the no-hair theorems, the frequencies and damping times of these modes are entirely determined by the mass and angular momentum of the final Kerr black hole. A detection of multiple ringdown modes would potentially allow us to test the no-hair theorem from observational data. The parameters which determine whether sub-dominant ringdown modes can be detected are primarily the overall signal-to-noise ratio present in the ringdown signal, and on the amplitude of the subdominant mode with respect to the dominant mode. In this paper, we use Bayesian inference to determine the detectability of a subdominant mode in a set of simulated analytical ringdown signals. Focusing on the design sensitivity of the Advanced LIGO detectors, we systematically vary the signal-to-noise ratio of the ringdown signal, and the mode amplitude ratio in order to determine what kind of signals are promising for performing black hole spectroscopy.