Spontaneous Scalarization Research Articles

Inspiral gravitational waveforms from compact binary systems in Horndeski gravity

In a subclass of Horndeski theories with the speed of gravity equivalent to that of light, we study gravitational radiation emitted during the inspiral phase of compact binary systems. We compute the waveform of scalar perturbations under a post-Newtonian expansion of energy-momentum tensors of pointlike particles that depend on a scalar field. This scalar mode not only gives rise to breathing and longitudinal polarizations of gravitational waves, but it is also responsible for scalar gravitational radiation in addition to energy loss associated with transverse and traceless tensor polarizations. We calculate the Fourier-transformed gravitational waveform of two tensor polarizations under a stationary phase approximation and show that the resulting waveform reduces to the one in a parametrized post-Einsteinian (ppE) formalism. The ppE parameters are directly related to a scalar charge in the Einstein frame, whose existence is crucial to allow the deviation from general relativity (GR). We apply our general framework to several concrete theories and show that a new theory of spontaneous scalarization with a higher-order scalar kinetic term leaves interesting deviations from GR that can be probed by the observations of gravitational waves emitted from neutron star--black hole binaries. If the scalar mass exceeds the order of typical orbital frequencies $\ensuremath{\omega}\ensuremath{\simeq}{10}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{eV}$, which is the case for a recently proposed scalarized neutron star with a self-interacting potential, the gravitational waveform practically reduces to that in GR.

Curvature induced scalarization of Kerr-Newman black hole spacetimes

With certain nonminimal coupling between a massless scalar field and the Gauss-Bonnet curvature invariant in the extended scalar-tensor-Gauss-Bonnet (ESTGB) field theory, tachyonic instability of the Kerr-Newman (KN) black hole is promoted. Critical spin and charge for the onset of the spontaneous scalarization phenomenon for the KN black hole are calculated in the infinitely large coupling limit. Then the analytical formula for the coupling-strength-dependent critical existence line is obtained for the black-hole-scalar-field configuration in a finite large coupling regime. Moreover, numerical methods are used to perform threshold curves that are boundaries between bald KN black holes and their hairy counterparts. Intriguingly, we get to know the KN black hole can be scalarized in the vanishing spin limit in ESTGB theory.

Tachyonic instability of Reissner-Nordström-Melvin black holes in Einstein-Maxwell-scalar theory

In the framework of Einstein-Maxwell-scalar theory, we studied scalar field perturbations of Reissner-Nordström-Melvin (RNM) black holes, which describes the RN black holes immersed in a uniform magnetic field. Due to the coupling to the Maxwell term, the scalar field acquires an effective mass square which, in the presence of the magnetic field, will become negative somewhere outside the horizon for either sign of the coupling constant α, thus triggering the tachyonic instability and leading to spontaneous scalarization when α is large enough. The magnetic field has significant influences on the waveforms and the onset of the instability, which differs for different sign of α. Effects of the black hole charge on the instability are also studied.

Magnetic-induced spontaneous scalarization in dynamical Chern–Simons gravity

In the framework of the dynamical Chern–Simons gravity, we study the scalar field perturbations of the Reissner–Nordström–Melvin spacetime, which describes a charged black hole permeated by a uniform magnetic field. In the presence of the magnetic field, the scalar field acquires an effective mass whose square takes negative value in the half domain of the angular direction. This inevitably introduces the tachyonic instability and associated spontaneous scalarization as long as the coupling constant between the scalar field and the Chern–Simons invariant exceeds a threshold value. We study the object pictures of the time evolutions of the scalar field perturbations at the linear level, and find that the presence of the magnetic field will dramatically change the waveforms and associated ringdown modes. Nonlinear evolutions for the unstable perturbations are also performed in the decoupling limit, which demonstrate the scalar cloud as the final fate. Influences of the coupling constant and the black hole charge on the wave dynamics are also studied.

Analytical Approximate Solutions for Scalarized AdS Black Holes

The spontaneous scalarization of Schwarzscild-AdS is investigated in the Einstein-scalar-Gauss–Bonnet (ESGB) theory. Firstly, we construct scalarized AdS black holes numerically. Secondly, making use of the homotopy analysis method (HAM), we obtain analytical approximate solutions for scalarized AdS black holes in the ESGB theory. It is found that scalarized AdS black holes constructed numerically are consistent with analytical approximate solutions in the whole space.

Multiscalar Gauss-Bonnet gravity: Scalarized black holes beyond spontaneous scalarization

Recently, a new nonlinear mechanism for black hole scalarization, different from the standard spontaneous scalarization, was demonstrated to exist for scalar Gauss-Bonnet theories in which no tachyonic instabilities can occur. Thus the Schwarzschild black hole is linearly stable but instead nonlinear instability can kick in. In the present paper we expand on this idea in the case of multiscalar Gauss-Bonnet gravity with exponential coupling functions of third and fourth leading order in the scalar field. The main motivation comes from the fact that these theories admit hairy compact objects with zero scalar charge, thus zero scalar-dipole radiation, which automatically evades the binary pulsar constraints on the theory parameters. We demonstrate numerically the existence of scalarized black holes for both coupling functions and for all possible maximally symmetric scalar field target spaces. The thermodynamics and the stability of the obtained solution branches is also discussed.

Spontaneous nonlinear scalarization of Kerr black holes

As it became well known in the past years, Einstein-scalar-Gauss-Bonnet (EsGB) theories evade no-hair theorems and allow for scalarized compact objects including black holes (BH). The coupling function that defines the theory is the main character in the process and nature of scalarization. With the right choice, the theory becomes an extension of general relativity (GR) in the sense any solution to the GR field equations remains a solution in the EsGB theory, but it can destabilize if a certain threshold value of the spacetime curvature is exceeded. Thus BHs can spontaneously scalarized. The most studied driving mechanism to this phenomenon is a tachyonic instability due to an effective negative squared mass for the scalar field. However, even when the coupling is chosen such that this mass is zero, higher order terms with respect to the scalar field can lead to what is coined nonlinear scalarization. In this paper we investigate how Kerr BHs spontaneously scalarize by evolving the scalar field on a fixed background via solving the nonlinear Klein-Gordon equation. We consider two different coupling functions with higher order terms, one that yields a non-zero effective mass and another that does not. We sweep through the Kerr parameter space in its mass and spin and obtain the scalar charge by the end of the evolution when the field settles in an equilibrium stationary state. When there is no tachyonic instability present, there is no probe limit in which the BH scalarizes with zero charge, i.e. there is a gap between bald and hairy BHs and they only connect when the mass goes to zero together with the charge.

Spin-charge induced spontaneous scalarization of Kerr-Newman black holes

We investigate the tachyonic instability of Kerr-Newman (KN) black holes in the Einstein-Maxwell-scalar (EMS) theory with a positive coupling parameter $\alpha$. This corresponds to exploring the onset of spontaneous scalarization for KN black holes. For this purpose, we use the hyperboloidal foliation method (HFM) to solve the linearized scalar equation numerically. We obtain a 3D graph [$\log_{10}\alpha(a,Q)$] which indicates the onset surface for spontaneous scalarization of KN black holes in the EMS theory. We find that there is no lower bound on the rotational parameter $a$, but its upper bound is given by $M^2-Q^2 \ge a^2$. Also, we confirm that the high rotation enhances spontaneous scalarization of KN black holes in the EMS theory.

Instability of de-Sitter black hole with massive scalar field coupled to Gauss–Bonnet invariant and the scalarized black holes

The black hole scalarization in a special Einstein-scalar–Gauss–Bonnet (EsGB) gravity has been widely investigated in recent years. Especially, the spontaneous scalarization of scalar-free black hole in de-Sitter (dS) spacetime possesses interesting features due to the existence of cosmological horizon. In this work, firstly, we focus on the massive scalar field perturbation on Schwarzschild dS (SdS) black hole in a special EsGB theory. By analyzing the fundamental QNM frequency and time evolution of the scalar field perturbation, we figure out the unstable/stable regions in (Lambda ,alpha )-plane as well as in (m,alpha )-plane for various perturbation modes, where Lambda , alpha and m denote the cosmological constant, the GB coupling strength and the mass of scalar field, respectively. Then by solving the static perturbation equation, we analyze the bifurcation point at which the SdS black hole supports spherical scalar clouds, and we find that the bifurcation points match well with alpha _c on the border of unstable/stable region. Finally, after addressing that the scalarised solutions could only emerge from the scalar could with node kge 1. we explicitly construct the scalarized hairy solutions for different scalar masses and compare the profile of scalar field to the corresponding scalar clouds.

Shrouded black holes in Einstein-Gauss-Bonnet gravity

We study black holes in a modified gravity scenario involving a scalar field quadratically coupled to the Gauss-Bonnet invariant. The scalar is assumed to be in a spontaneously broken phase at spatial infinity due to a bare Higgs-like potential. For a proper choice of sign, the non-minimal coupling to gravity leads to symmetry restoration near the black hole horizon, prompting the development of the scalar wall in its vicinity. The wall thickness depends on the bare mass of the scalar and can be much smaller than the Schwarzschild radius. In a weakly coupled regime, the quadratic coupling to the Gauss-Bonnet invariant effectively becomes linear, and no walls are formed. We find approximate analytical solutions for the scalar field in the test field regime, and obtain numerically static black hole solutions within this setup. We discuss cosmological implications of the model and show that it is fully consistent with the existence of an inflationary stage, unlike the spontaneous scalarization scenario assuming the opposite sign of the non-minimal coupling to gravity. Our model predicts the speed of gravitational waves to be extremely close to unity, - in a comfortable agreement with the observation of the GW170817 event and its electromagnetic counterpart.

Dynamical spontaneous scalarization in Einstein-Maxwell-scalar models in anti–de Sitter spacetime

The phenomenon of spontaneous scalarization of charged black holes has attracted a lot of attention. In this work, we study the dynamical process of the spontaneous scalarization of charged black hole in asymptotically anti-de Sitter spacetimes in Einstein-Maxwell-scalar models. Including various non-minimal couplings between the scalar field and Maxwell field, we observe that an initial scalar-free configuration suffers tachyonic instability and both the scalar field and the black hole irreducible mass grow exponentially at early times and saturate exponentially at late times. For fractional couplings, we find that though there is negative energy distribution near the black hole horizon, the black hole horizon area never decreases. But when the parameters are large, the evolution endpoints of linearly unstable bald black holes will be spacetimes with naked singularity and the cosmic censorship is violated. The effects of the black hole charge, cosmological constant and coupling strength on the dynamical scalarization process are studied in detail. We find that large enough cosmological constant can prevent the spontaneous scalarization.

Spin-charge induced scalarization of Kerr-Newman black-hole spacetimes

It has recently been demonstrated that Reissner-Nordström black holes in composed Einstein-Maxwell-scalar field theories can support static scalar field configurations with a non-minimal negative coupling to the Maxwell electromagnetic invariant of the charged spacetime. We here reveal the physically interesting fact that scalar field configurations with a non-minimal positive coupling to the spatially-dependent Maxwell electromagnetic invariant mathcal{F} ≡ FμνFμν can also be supported in black-hole spacetimes. Intriguingly, it is explicitly proved that the positive-coupling black-hole spontaneous scalarization phenomenon is induced by a non-zero combination a ∙ Q ≠ 0 of both the spin a ≡ J/M and the electric charge Q of the central supporting black hole. Using analytical techniques we prove that the regime of existence of the positive-coupling spontaneous scalarization phenomenon of Kerr-Newman black holes with horizon radius r+(M, a, Q) and a non-zero electric charge Q (which, in principle, may be arbitrarily small) is determined by the critical onset line (a/r+)critical = sqrt{2} − 1. In particular, spinning and charged Kerr-Newman black holes in the composed Einstein-Maxwell-scalar field theory are spontaneously scalarized by the positively coupled fields in the dimensionless charge regime 0<frac{Q}{M}le sqrt{2sqrt{2}-2} if their dimensionless spin parameters lie above the critical onset line frac{a(Q)}{M}ge {left[frac{a(Q)}{M}right]}_{mathrm{critical}}=frac{1+sqrt{1-2left(2-sqrt{2}right){left(Q/Mright)}^2}}{2sqrt{2}} .

Spin-induced scalarization of Kerr-Newman black holes in Einstein-Maxwell-scalar theory

In this paper, we consider the tachyonic instability of Kerr-Newman (KN) black holes in the Einstein-Maxwell-scalar (EMS) theory with nonminimal negative scalar coupling to Maxwell term, and then obtain a bound $(\frac{a}{r_+}\geq0.4142)$ for spin parameter $a$ of KN black hole in the limit of coupling constant $\alpha\rightarrow-\infty$ by using analytical method. In addition, we perform a $(2+1)$-dimensional time evolution of linearized scalar field perturbation on the KN black hole background by implementing the hyperboloidal foliation method numerically in the EMS theory. It recovers the \textit{spontaneous scalarization} phenomenon for KN black hole in some certain regions of the parameter spaces. We further plot corresponding threshold curves $\alpha(a)$ which describe a boundary between bald KN black holes and scalarized spinning black holes in the EMS theory.

Spin-induced dynamical scalarization, descalarization, and stealthness in scalar-Gauss-Bonnet gravity during a black hole coalescence

Particular couplings between a scalar field and the Gauss-Bonnet invariant lead to spontaneous scalarization of black holes. Here we continue our work on simulating this phenomenon in the context of binary black hole systems. We consider a negative coupling for which the black-hole spin plays a major role in the scalarization process. We find two main phenomena: (i) dynamical descalarization, in which initially scalarized black holes form an unscalarized remnant, and (ii) dynamical scalarization, whereby the late merger of initially unscalarized black holes can cause scalar hair to grow. An important consequence of the latter case is that modifications to the gravitational waveform due to the scalar field may only occur post-merger, as its presence is hidden during the entirety of the inspiral. However, with a sufficiently strong coupling, we find that scalarization can occur before the remnant has even formed. We close with a discussion of observational implications for gravitational-wave tests of general relativity.

Extend Bekenstein’s theorem to Einstein–Maxwell-scalar theories with a scalar potential

The Bekenstein’s theorem allows us to generate an Einstein-conformal scalar solution from a single Einstein-ordinary scalar solution. In this article, we extend this theorem to the Einstein–Maxwell-scalar (EMS) theory with a non-minimal coupling between the scalar and Maxwell field when a scalar potential is also included. As applications of this extended theorem, the well-known static dilaton solution and rotating solution with a specific coupling between dilaton and Maxwell field are considered, and new conformal dilaton black hole solutions are found. The Noether charges, such as mass, electric charge, and angular momentum, are compared between the old and new black hole solutions connected by conformal transformations, and they are found conformally invariant. We speculate that the theorem may be useful in the computations of metric perturbations and spontaneous scalarization of black holes in the Einstein–Maxwell-conformal-scalar theory since they can be mapped to the corresponding EMS theories, which have been investigated in detail.

Dynamical spontaneous scalarization in Einstein-Maxwell-scalar theory * *Supported by the National Key R&D Program of China (2020YFC2201400), the Natural Science Foundation of China (11805083, 11905083, 12005077) and Guangdong Basic and Applied Basic Research Foundation (2021A1515012374)

We study the linear instability and nonlinear dynamical evolution of the Reissner-Nordström (RN) black hole in the Einstein-Maxwell-scalar theory in asymptotic flat spacetime. We focus on the coupling function , which facilitates both scalar-free RN and scalarized black hole solutions. We first present the evolution of system parameters during dynamic scalarization. For parameter regions in which spontaneous scalarization occurs, we observe that the evolution of the scalar field at the horizon is dominated by the fundamental unstable mode from linear analysis at early times. At late times, the nonlinear evolution can be considered to be the perturbation of scalarized black holes.

Constraining spontaneous black hole scalarization in scalar-tensor-Gauss-Bonnet theories with current gravitational-wave data

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 $\ensuremath{\lambda}$ 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---whose primary black hole has a spin that is bounded to be small, and whose signal shows no evidence of a scalarized primary---to rule out a narrow region of the parameter space. In particular, we find that values of $\ensuremath{\lambda}\ensuremath{\in}[56,96]\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ 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.

Spontaneous scalarization in (A)dS gravity at zero temperature

We study spontaneous scalarization of electrically charged extremal black holes in D ≥ 4 spacetime dimensions. Such a phenomenon is caused by the symmetry breaking due to quartic interactions of the scalar — Higgs potential and Stueckelberg interaction with electromagnetic and gravitational fields, characterized by the couplings a and b, respectively. We use the entropy representation of the states in the vicinity of the horizon, apply the inverse attractor mechanism for the scalar field, and analyze analytically the thermodynamic stability of the system using the laws of thermodynamics. As a result, we obtain that the scalar field condensates on the horizon only in spacetimes which are asymptotically non-flat, Λ ≠ 0 (dS or AdS), and whose extremal black holes have non-planar horizons k = ±1, provided that the mass m of the scalar field belongs to a mass interval (area code) different for each set of the boundary conditions specified by (Λ, k). A process of scalarization describes a second order phase transition of the black hole, from the extremal Reissner-Nordström (A)dS one, to the corresponding extremal hairy one. Furthermore, for the transition to happen, the interaction has to be strong enough, and all physical quantities on the horizon depend at most on the effective Higgs-Stueckelberg interaction am2− 2b. Most of our results are general, valid for any parameter and any spacetime dimension.

Constraining scalar-tensor theories using neutron star mass and radius measurements

We use neutron star mass and radius measurements to constrain the spontaneous scalarization phenomenon in scalar-tensor theories using Bayesian analysis. Neutron star structures in this scenario can be significantly different from the case of general relativity, which can be used to constrain the theory parameters. We utilize this idea to obtain lower bounds on the coupling parameter $\beta$ for the case of massless scalars. These constraints are currently weaker than the ones coming from binary observations, and they have relatively low precision due to the approximations in our method. Nevertheless, our results clearly demonstrate the power of the mass-radius data in testing gravity, and can be further improved with future observations. The picture is different for massive scalars, for which the same data is considerably less effective in constraining the theory parameters in an unexpected manner. We identify the main reason for this to be a large high-likelihood region in the parameter space where deviations from general relativity are relatively small. We hope this initial study to be an invitation to use neutron star structure measurements more commonly to test alternative theories in general.

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.