No-hair Research Articles

Parity violation in spin-precessing binaries: Gravitational waves from the inspiral of black holes in dynamical Chern-Simons gravity

Spin precession in compact binaries is intricately tuned to the multipole structure of the underlying bodies. For black holes, violations of the no-hair theorems induced by modifications to general relativity correct the precession dynamics, which in turn imprints onto the amplitude and phase modulations of the gravitational waves emitted by the binary. Recently, the spin precession equations were derived up to second order in spin for dynamical Chern-Simons (dCS) gravity, a parity-violating modified theory of gravity. We here solve these equations and construct, for the first time, analytic expressions for the time- and frequency-domain gravitational waves emitted in the quasicircular inspiral of spin-precessing black hole binaries in a modified theory of gravity using the post-Newtonian approximation. Working within the small coupling approximation and using multiple scale analysis, we show that the corrections to the nutation phase enter at relative first post-Newtonian (1PN) order, and the corrections to the precession angle and Thomas phase enter at relative 0PN order. Making use of the stationary phase approximation and shifted uniform asymptotics, we find that the Fourier phase of the waveform is characterized by three modifications: two due to the backreaction of the precession dynamics onto the spin-orbit and spin-spin couplings that enter at 1.5PN and 2PN orders, and a 2PN modification due to the emission of dipole radiation. We also find that backreaction of the precession dynamics forces the dCS corrections to the Fourier amplitude to enter at 0PN order, as opposed to 2PN order, as expected for spin-aligned binaries. Our work lays the first foundational stones to build an inspiral-merger-ringdown phenomenological model for spin-precessing binaries in a modified theory of gravity.

Black hole solutions in scalar-tensor symmetric teleparallel gravity

Symmetric teleparallel gravity is constructed with a nonzero nonmetricity tensor while both torsion and curvature are vanishing. In this framework, we find exact scalarised spherically symmetric static solutions in scalar-tensor theories built with a nonminimal coupling between the nonmetricity scalar and a scalar field. It turns out that the Bocharova-Bronnikov-Melnikov-Bekenstein solution has a symmetric teleparallel analogue (in addition to the recently found metric teleparallel analogue), while some other of these solutions describe scalarised black hole configurations that are not known in the Riemannian or metric teleparallel scalar-tensor case. To aid the analysis we also derive no-hair theorems for the theory. Since the symmetric teleparallel scalar-tensor models also include f(Q) gravity, we shortly discuss this case and further prove a theorem which says that by imposing that the metric functions are the reciprocal of each other (grr = 1/gtt ), the f(Q) gravity theory reduces to the symmetric teleparallel equivalent of general relativity (plus a cosmological constant), and the metric takes the (Anti)de-Sitter-Schwarzschild form.

Radial perturbations of scalar-Gauss-Bonnet black holes beyond spontaneous scalarization

Spontaneous scalarization of black holes in scalar-Gauss-Bonnet (sGB) gravity is a very interesting phenomenon allowing black holes to circumvent the no-hair theorem and acquire scalar hair while leaving the weak field regime of the theory practically unaltered. It was recently shown that if we allow for a different form of the coupling between the scalar field and the Gauss-Bonnet invariant, a new type of scalarization is possible beyond the standard one that can be excited only nonlinearly. In this case the spectrum of black hole solutions can be more complicated, naturally opening the question about their stability. The goal of the present paper is to study this question including the possible loss of hyperbolicity of the radial perturbation equation. We show that one of the nonlinearly scalarized phases of the Schwarzschild black hole can be stable and hyperbolic for large enough black hole masses. These results establish the studied hairy black holes as viable astrophysical candidates.

Testing Horndeski Gravity from EHT Observational Results for Rotating Black Holes

The Event Horizon Telescope (EHT) collaboration recently unveiled the first image of the supermassive black hole M87*, which exhibited a ring of angular diameter θ d = 42 ± 3 μas, a circularity deviation of ΔC ≤ 0.1, and also inferred a black hole mass of M = (6.5 ± 0.7) × 109 M ⊙. This provides a new window onto tests of theories of gravity in the strong-field regime, including probes of violations of the no-hair theorem. It is widely believed that the Kerr metric describes astrophysical black holes, as encapsulated in the critical but untested no-hair theorem. Modeling Horndeski gravity black holes—with an additional hair parameter h besides the mass M and spin a of the Kerr black hole—as the supermassive black hole M87*, we observe that to be a viable astrophysical black hole candidate, the EHT result constrains the (a, h) parameter space. However, a systematic bias analysis indicates that rotating Horndeski black hole shadows may or may not capture Kerr black hole shadows, depending on the parameter values; the latter is the case over a substantial part of the constrained parameter space, allowing Horndeski gravity and general relativity to be distinguishable in the said space, and opening up the possibility of potential modifications to the Kerr metric.

Investigating strong gravitational lensing effects by supermassive black holes with Horndeski gravity

We study gravitational lensing in strong-field limit by a static spherically symmetric black hole in quartic scalar field Horndeski gravity having additional hair parameter q, evading the no-hair theorem. We find an increase in the deflection angle alpha _D, photon sphere radius x_{ps}, and angular position theta _{infty } that increases more quickly while angular separation s more slowly, but the ratio of the flux of the first image to all other images r_{mag} decreases rapidly with increasing magnitude of the hair q. We also discuss the astrophysical consequences in the supermassive black holes at the centre of several galaxies and note that the black holes in Horndeski gravity can be quantitatively distinguished from the Schwarzschild black hole. Notably, we find that the deviation Delta theta _{infty } of black holes in Horndeski gravity from their general relativity (GR) counterpart, for supermassive black holes Sgr A* and M87*, for q=-0.2, respectively, can reach as much as 2.4227~mu as and 1.82026~mu as while Delta s is about 0.04650~mu as for Sgr A* and 0.03493~mu as for M87*. The ratio of the flux of the first image to all other images suggest that the Schwarzschild images are brighter than those of the black holes in Horndeski gravity, wherein the deviation |Delta r_{mag}| is as much as 0.70673. The results suggest that observational tests of hairy black holes in Horndeski gravity are indeed feasible. Taking the supermassive black holes Sgr A* and M87* as the lens, we also compare our hairy Horndeski black holes observable signatures with those of the neutral Horndeski black holes, Galileon black holes and charged Horndeski black holes. It turns out that although it is possible to detect some effects of the strong deflection lensing by the hairy Horndeski black holes and other black holes with the Event Horizon Telescope (EHT) observations, but it is unconvincing to discern these black holes as deviations are {mathcal {O}}(mu as). We also find that the shadow size is consistent with EHT observation if the deviation parameter q in (-0.281979,0)

Scalarized black holes in teleparallel gravity

Black holes play a crucial role in the understanding of the gravitational interaction. Through the direct observation of the shadow of a black hole by the event horizon telescope and the detection of gravitational waves of merging black holes we now start to have direct access to their properties and behaviour, which means the properties and behaviour of gravity. This further raised the demand for models to compare with those observations.In this respect, an important question regarding black holes properties is to know if they can support “hairs”. While this is famously forbidden in general relativity, in particular for scalar fields, by the so-called no-hair theorems, hairy black holes have been shown to exist in several class of scalar-tensor theories of gravity.In this article we investigate the existence of scalarized black holes in scalar-torsion theories of gravity.On one hand, we find exact solutions for certain choices of couplings between a scalar field and the torsion tensor of a teleparallel connection and certain scalar field potentials, and thus proof the existence of scalarized black holes in these theories.On the other hand, we show that it is possible to establish no-scalar-hair theorems similar to what is known in general relativity for other choices of these functions.

Tidal deformation of dynamical horizons in binary black hole mergers

An important physical phenomenon that manifests itself during the inspiral of two orbiting compact objects is the tidal deformation of each under the gravitational influence of its companion. In the case of binary neutron star mergers, this tidal deformation and the associated Love numbers have been used to probe properties of dense matter and the nuclear equation of state. Non-spinning black holes on the other hand have a vanishing (field) tidal Love number in General Relativity. This pertains to the deformation of the asymptotic gravitational field. In certain cases, especially in the late stages of the inspiral phase when the black holes get close to each other, the source multipole moments might be more relevant in probing their properties and the No-Hair conjecture; contrastingly, these Love numbers do not vanish. In this paper, we track the source multipole moments in simulations of several binary black hole mergers and calculate these Love numbers. We present evidence that, at least for modest mass ratios, the behavior of the source multipole moments is universal.

Black hole spectroscopy horizons for current and future gravitational wave detectors

Black hole spectroscopy is the proposal to observe multiple quasinormal modes in the ringdown of a binary black hole merger. In addition to the fundamental quadrupolar mode, overtones and higher harmonics may be present and detectable in the gravitational wave signal, allowing for tests of the no-hair theorem. We analyze in detail the strengths and weaknesses of the standard Rayleigh criterion supplied with a Fisher matrix error estimation, and we find that the criterion is useful, but too restrictive. Therefore we motivate the use of a conservative high Bayes factor threshold to obtain the black hole spectroscopy horizons of current and future detectors, i.e., the distance (averaged in sky location and binary inclination) up to which one or more additional modes can be detected and confidently distinguished from each other. We set up all of our searches for additional modes starting at $t = 10(M_1+M_2)$ after the peak amplitude in simulated signals of circular nonspinning binaries. An agnostic multimode analysis allows us to rank the subdominant modes: for nearly equal mass binaries we find $(\ell, m, n) = (2,2,1)$ and $(3,3,0)$ and, for very asymmetric binaries, $(3,3,0)$ and $(4,4,0)$, for the secondary and tertiary modes, respectively. At the current estimated rates for heavy stellar mass binary black hole mergers, with primary masses between 45 and 100 solar masses, we expect an event rate of mergers within our conservative estimate for the $(2,2,1)$ spectroscopy horizon of $0.03 - 0.10\ {\rm yr}^{-1}$ for LIGO at design sensitivity and $(0.6 - 2.4) \times 10^3\ {\rm yr}^{-1}$ for the future third generation ground-based detector Cosmic Explorer.

Retesting the no-hair theorem with GW150914

For a distorted black hole (BH), its ringdown waveform is a superposition of quasi-normal modes (QNMs). In general relativity (GR), the lower order QNM frequencies and damping rates can be well approximated by a polynomial of BH’s dimensionless spin and overall scaled by BH’s mass. That is to say, we can test the no-hair theorem of BH in GR model-independently by allowing not only an overall fractional deviation (as M. Isi et al. did) but also a set of fractional deviation for every coefficient. In the paper, we will apply the latter method to retest the no-hair theorem with GW150914 and probe hairs’ behaviors if hairs exist. Eventually, we find the data favors GR.

Anisotropic hyperbolic inflation for a model of two scalar and two vector fields

In this paper, we extend a recent proposed model of two scalar and two vector fields to a hyperbolic inflation scenario, in which the field space of two scalar fields is a hyperbolic space instead of a flat space. In this model, one of the scalar fields is assumed to be a radial field, while the other is set as an angular field. Furthermore, both scalar fields will be coupled to two different vector fields, respectively. As a result, we are able to obtain a set of exact Bianchi type I solutions to this model. Stability analysis is also performed to show that this set of anisotropic solutions is indeed stable and attractive during the inflationary phase. This result indicates that the cosmic no-hair conjecture is extensively violated in this anisotropic hyperbolic inflation model.

The non-Kerr black hole with acceleration

The no-hair theorem can be tested in the strong gravity regime by using the top–bottom approach and the bottom–top approach. The non-Kerr spacetime of the later approach is an ideal framework to do the tests in the region very close to the black holes. In this work, we propose a non-Kerr black hole metric (and its charged extension) that is accelerating as well. These new objects are studied for their basic properties and thermodynamics.

Ladder symmetries of black holes. Implications for love numbers and no-hair theorems

It is well known that asymptotically flat black holes in generalrelativity have a vanishing static, conservative tidal response. We show that this is a result of linearly realized symmetries governingstatic (spin 0,1,2)perturbations around black holes. The symmetries have a geometric origin: in the scalar case, they arise from the (E)AdS isometries of a dimensionally reduced black hole spacetime. Underlying the symmetries is a ladder structure which can be used to construct the full tower of solutions,and derive their general properties: (1) solutions that decay withradius spontaneously break the symmetries, and mustdiverge at the horizon;(2) solutions regular at the horizon respect the symmetries, andtake the form of a finite polynomial that grows with radius.Taken together, these two properties imply that static response coefficients — and in particular Love numbers — vanish. Moreover, property (1) is consistent with the absence of black holes with linear (perturbative) hair. We also discuss the manifestation of these symmetries in the effective point particle description of a black hole, showing explicitly that for scalar probesthe worldline couplings associated with a non-trivial tidal response and scalar hair must vanish in order for the symmetries to be preserved.

Electromagnetic signatures of strong-field gravity from accreting black-holes

Observations of galactic nuclei help us to test General Relativity. Whereas the No-hair Theorem states that classical, isolated black holes eventually settle to a stationary state that can be characterized by a small number of parameters, cosmic black holes are neither isolated nor steady. Instead, they interact with the environment and evolve on vastly different time-scales. Therefore, the astrophysically realistic models require more parameters, and their values likely change in time. New techniques are needed in order to allow us to obtain independent constraints on these additional parameters. In this context, non-electromagnetic messengers have emerged and a variety of novel electromagnetic observations is going to supplement traditional techniques in the near future. In this outline, we summarize several fruitful aspects of electromagnetic signatures from accretion disks in strong-gravity regime in the outlook of upcoming satellite missions and ground-based telescopes. As an interesting example, we mention a purely geometrical effect of polarization angle changes upon light propagation, which occurs near the black hole event horizon. Despite that only numerical simulations can capture the accretion process in a realistic manner, simplified toy-models and semi-analytical estimates are useful to understand complicated effects of strong gravity near the event horizon of a rotating black hole, and especially within the plunging region below the innermost stable circular orbit.

Cosmic no-hair conjecture and inflation with an SU(3) gauge field

We study inflationary universes with an SU(3) gauge field coupled to an inflaton through a gauge kinetic function. Although the SU(3) gauge field grows at the initial stage of inflation due to the interaction with the inflaton, nonlinear self-couplings in the kinetic term of the gauge field become significant and cause nontrivial dynamics after sufficient growth. We investigate the evolution of the SU(3) gauge field numerically and reveal attractor solutions in the Bianchi type I spacetime. In general cases where all the components of the SU(3) gauge field have the same magnitude initially, they all tend to decay eventually because of the nonlinear self-couplings. Therefore, the cosmic no-hair conjecture generically holds in a mathematical sense. Practically, however, the anisotropy can be generated transiently in the early universe, even for an isotropic initial condition. Moreover, we find particular cases for which several components of the SU(3) gauge field survive against the nonlinear self-couplings. It occurs due to flat directions in the potential of a gauge field for Lie groups whose rank is higher than one. Thus, an SU(2) gauge field has a specialty among general non-Abelian gauge fields.

Compactified holographic conformal order

We study holographic conformal order compactified on S3. The corresponding boundary CFT4 has a thermal phase with a nonzero expectation value of a certain operator. The gravitational dual to the ordered phase is represented by a black hole in asymptotically AdS5 that violates the no-hair theorem. While the compactification does not destroy the ordered phase, it does not cure its perturbative instability: we identify the scalar channel QNM of the hairy black hole with Im[w]>0. On the contrary, we argue that the disordered thermal phase of the boundary CFT is perturbatively stable in holographic models of Einstein gravity and scalars.

X-Ray Quasi-periodic Eruptions Driven by Star–Disk Collisions: Application to GSN069 and Probing the Spin of Massive Black Holes

Abstract X-ray quasi-periodic eruptions (QPEs) were discovered recently in active galaxies with an unknown driving mechanism. Under the assumption that QPEs are caused by star–disk collisions, we adopt full relativistic method and show that both the orbital parameters of the star and also the mass and spinning of the massive black hole (MBH) can be revealed by using the time of arrival (TOA) of the QPEs. By applying the model to the observed QPEs of GSN069, we find that the star is in a near-circular orbit ( e • = 0.05 − 0.02 + 0.02 ) with a semimajor axis of ∼ 365 − 49 + 54 r g around an MBH with M • = 3.0 − 0.6 + 0.9 × 10 5 M ⊙ . The alternative short and long recurring time of the QPEs of GSN069 can be well explained by the small eccentricity and the orbital precession of the star. We find that the QPEs of GSN069 are possibly driven by a striped stellar core colliding with accretion disk after a partial tidal disruption event around the MBH. For GSN069-like galaxies, if continuous X-ray monitoring of QPE events can be accumulated with uncertainties of TOA ≲100–150 s, the spin of the MBH can be constrained by fitting to QPEs. Our results show that the timing of QPEs can provide a unique probe for measuring the spinning of the MBH and tests of the no-hair theorem.

Testing no-hair theorem by quasi-periodic oscillations: thequadrupole of GRO J1655–40

We perform an observational test of no-hair theorem usingquasi-periodic oscillations within the relativistic precession model. Twowell motivated metrics we apply are Kerr-Q and Hartle-Thorne metrics inwhich the quadrupole is the parameter that possibly encodes deviations fromthe Kerr black hole. The expressions for the quasi-periodic frequencies arederived before comparing the models with the observation. We encounter adegeneracy in constraining spin and quadrupole parameters that makes itdifficult to measure their values. In particular, we here propose a noveltest of no-hair theorem by adapting the Hartle-Thorne metric. We complement our study by doing a model comparison. We findthat there is strong evidence that Kerr black hole is the source of the central object in GROJ1655–40 given the present observational precisions.

Existence and uniqueness of asymptotically flat toric gravitational instantons

We prove uniqueness and existence theorems for four-dimensional asymptotically flat, Ricci-flat, gravitational instantons with a torus symmetry. In particular, we prove that such instantons are uniquely characterised by their rod structure, which is data that encodes the fixed point sets of the torus action. Furthermore, we establish that for every admissible rod structure there exists an instanton that is smooth up to possible conical singularities at the axes of symmetry. The proofs involve adapting the methods that are used to establish black hole uniqueness theorems, to a harmonic map formulation of Ricci-flat metrics with torus symmetry, where the target space is directly related to the metric (rather than auxiliary potentials). We also give an elementary proof of the nonexistence of asymptotically flat toric half-flat instantons. Finally, we derive a general set of identities that relate asymptotic invariants such as the mass to the rod structure.

Regular scalar charged clouds around a Reissner-Nordstrom black hole and no-hair theorems

In this work we reanalyze the possibility of finding bound states (scalar clouds) of a test, charged and complex-valued scalar field with mass and charge q in the background of a Reissner-Nordstrom black hole (RNBH). In order to determine the existence of such scalar clouds we impose suitable regularity conditions for the scalar field at the event horizon. We find numerical evidence for the absence of such clouds in the subextremal and extremal RNBH when the field is massive but not self-interacting. More importantly, we put forward a theorem that proves that such clouds cannot exist. On the other hand, when a suitable self-interacting potential is included, the theorem no longer applies, providing a heuristic justification behind the existence of charged clouds (Q-clouds) that were reported recently.

Science with the TianQin Observatory: Preliminary results on testing the no-hair theorem with extreme mass ratio inspirals

Constituted with a massive black hole and a stellar mass compact object, Extreme Mass Ratio Inspiral (EMRI) events hold unique opportunity for the study of massive black holes, such as by measuring and checking the relations among the mass, spin and quadrupole moment of a massive black hole, putting the no-hair theorem to test. TianQin is a planned space-based gravitational wave observatory and EMRI is one of its main types of sources. It is important to estimate the capacity of TianQin on testing the no-hair theorem with EMRIs. In this work, we use the analytic kludge waveform with quadrupole moment corrections and study how the quadrupole moment can be constrained with TianQin. We find that TianQin can measure the dimensionless quadrupole moment parameter with accuracy to the level of $10^{-5}$ under suitable scenarios. The choice of the waveform cutoff is found to have significant effect on the result: if the Schwarzschild cutoff is used, the accuracy depends strongly on the mass of the massive black hole, while the spin has negligible impact; if the Kerr cutoff is used, however, the dependence on the spin is more significant. We have also analyzed the cases when TianQin is observing simultaneously with other detectors such as LISA.