Black hole spontaneous scalarization has been attracting more and more attention as it circumvents the well-known no-hair theorems. In this work, we study the scalarization in Einstein-scalar-Gauss-Bonnet theory with a probe scalar field in a black hole background with different curvatures. We first probe the signal of black hole scalarization with positive curvature in different spacetimes. The scalar field in AdS spacetime could be formed easier than that in flat case. Then, we investigate the scalar field around AdS black holes with negative and zero curvatures. Comparing with negative and zero cases, the scalar field near AdS black hole with positive curvature could be much easier to emerge. And in negative curvature case, the scalar field is the most difficult to be bounded near the horizon.
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 …
We study the fully nonlinear dynamics of black hole spontaneous scalarizations in Einstein-Maxwell scalar theory with coupling function $f(ϕ)=e^{-bϕ^{2}}$, which can transform usual Reissner-Nordström Anti-de Sitter (RN-AdS) black holes into hairy black holes. Fixing the Arnowitt-Deser-Misner mass of the system, the initial scalar perturbation will destroy the original RN-AdS black hole and turn it into a hairy black hole provided that the constant $-b$ in the coupling function and the charge of the original black hole are sufficiently large, while the cosmological constant is small enough. In…
We study the process of fully nonlinear dynamical scalarization starting from a charged black hole or a naked singularity in asymptotically flat spacetime in the Einstein-Maxwell-dilaton theory. Initially the dilaton field is negligible compared to the gravitational and the Maxwell field. Then the dilaton field experiences an immediate growth, later it oscillates with damping amplitude and finally settles down to a finite value. For a hairy black hole develops from an original Reissner-Nordström black hole, since the dilaton oscillation and decay are almost independent of the coupling paramete…
We present a new family of exact black hole configurations, which is a solution to a generalized Einstein-Maxwell-Dilaton setup in arbitrary dimension. These solutions are asymptotically Lifshitz for any dynamical critical exponent $z\geq 1$. It turns out that the existence of a nontrivial scalar field is a direct consequence of breaking the spacetime isotropic scaling symmetry. This black hole family accepts various interesting limits that link it to well-known solutions in both the isotropic and anisotropic cases. We study the thermodynamics of these field configurations showing that the fir…
We review recent results on the existence of static black holes without spatial isometries in four spacetime dimensions and propose a general framework for their study. These configurations are regular on and outside a horizon of spherical topology. Two different mechanisms allowing for their existence are identified. The first one relies on the presence of a solitonic limit of the black holes; when the solitons have no spatial isometries, the black holes, being a non-linear bound state between the solitons and a horizon, inherit this property. The second one is related to black hole scalariza…
We investigate the possibility of spontaneous scalarization of static, spherically symmetric, and asymptotically flat black holes (BHs) in the Horndeski theory. Spontaneous scalarization of BHs is a phenomenon that the scalar field spontaneously obtains a nontrivial profile in the vicinity of the event horizon via the nonminimal couplings and eventually the BH possesses a scalar charge. In the theory in which spontaneous scalarization takes place, the Schwarzschild solution with a trivial profile of the scalar field exhibits a tachyonic instability in the vicinity of the event horizon, and evo…
We study the linear instability and the 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 $f(ϕ)=e^{-bϕ^2}$ which allows both the scalar-free RN solution and scalarized black hole solution. We first present the evolution of system parameters during dynamic scalarization. For parameter regions where spontaneous scalarization occurs, we find that the evolution of the scalar field at the horizon is dominated by the fundamental unstable mode from linear analysis at early times…
We analyze condensation behaviors of neutral scalar fields outside horizonless reflecting stars in the Einstein-Maxwell-scalar gravity. It was known that minimally coupled neutral scalar fields cannot exist outside horizonless reflecting stars. In this work, we consider non-minimal couplings between scalar fields and Maxwell fields, which is included to aim to trigger formations of scalar hairs. We analytically demonstrate that there is no hair theorem for small coupling parameters below a bound. For large coupling parameters above the bound, we numerically obtain regular scalar hairy configur…
We present the first fully nonlinear study on the accretion of scalar fields onto a seed black hole in anti-de Sitter spacetime in Einstein-Maxwell-scalar theory. Intrinsic critical phenomena in the dynamical transition between the bald and scalarized black holes are disclosed. In scalarizations, the transition is discontinuous and a metastable black hole acts as an attractor at the threshold. We construct a new physical mechanism to dynamically descalarize an isolated scalarized black hole. The first results on critical phenomena in descalarizations are revealed. The dynamical descalarization…
Critical phenomenon inside asymptotically flat black holes with spontaneous scalarization
Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences（亚洲太平洋理论物理中心，中国科学院大学）
We propose a class of higher-derivative gravities that can be viewed as the Gauss-Bonnet extension of the Starobinsky model. The theory admits the Minkowski spacetime vacuum whose linear spectrum consists of the graviton and a massive scalar mode. In addition to the usual Schwarzschild black hole, we use numerical analysis to establish that in some suitable mass range, new black holes carrying the massive scalar hair can emerge. The new black hole serves as a "wall" separating the naked spacetime singularity and wormholes in the parameter space of the scalar hair. Our numerical results also in…
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 {\it positive} coupling to the spatially-dependent Maxwell electromagnetic invariant ${\cal F}\equiv F_{μν}F^{μν}$ can also be supported in black-hole spacetimes. Intriguingly, it is explicitly proved that the positive-coupling b…
In the present paper we study models of neutron stars in a class of extended scalar-tensor Gauss-Bonnet (ESTGB) theories for which the scalar degree of freedom is exited only in the strong curvature regime. We show that in the framework of the ESTGB theories under consideration there exist new neutron star solutions which are formed via spontaneous scalarization of the general relativistic neutron stars. In contrast to the spontaneous scalarization in the standard scalar-tensor theories which is induced by the presence of matter, in our case the scalarization is induced by the spacetime curvat…
In certain classes of the scalar-Gauss-Bonnet theory strong spacetime curvature in the vicinity of neutron stars and black holes can spontaneously trigger scalarization in the compact object if the coupling strength of the scalar field to the Gauss-Bonnet invariant exceeds a critical value. Specifying on neutron stars, this threshold depends on the mass and equation of state. The presence of a companion will further influence the required coupling strength for scalarization, and thus, a stable hair can be installed at a lower magnitude of coupling for those neutron stars as members of binaries…
We study the spontaneous scalarization of a standard conducting charged sphere embedded in Maxwell-scalar models in flat spacetime, wherein the scalar field $ϕ$ is nonminimally coupled to the Maxwell electrodynamics. This setup serves as a toy model for the spontaneous scalarization of charged (vacuum) black holes in Einstein-Maxwell-scalar (generalized scalar-tensor) models. In the Maxwell-scalar case, unlike the black hole cases, closed-form solutions exist for the scalarized configurations. We compute these configurations for three illustrations of nonminimal couplings: one that \textit{exa…
In the presence of certain non-minimal couplings between a scalar field and the Gauss-Bonnet curvature invariant, Kerr black holes can scalarize, as long as they are spinning fast enough. This provides a distinctive violation of the Kerr hypothesis, occurring only for some high spin range. In this paper we assess if strong magnetic fields, that may exist in the vicinity of astrophysical black holes, could facilitate this distinctive effect, by bringing down the spin threshold for scalarization. This inquiry is motivated by the fact that self-gravitating magnetic fields, by themselves, can also…
In the simplest scalar-tensor theories, wherein the scalar field is non-minimally coupled to the Ricci scalar, spontaneous scalarization of electrovacuum black holes (BHs) does not occur. This ceases to be true in higher dimensional spacetimes, $d>4$. We consider the scalarization of the higher dimensional Reissner-Nordström BHs in scalar-tensor models and provide results on the zero modes for different $d$, together with an explicit construction of the scalarized BHs in $d=5$, discussing some of their properties. We also observe that a conformal transformation into the Einstein frame maps thi…
Spontaneous scalarization is a mechanism that endows relativistic stars and black holes with a nontrivial configuration only when their spacetime curvature exceeds some threshold. The standard way to trigger spontaneous scalarization is via a tachyonic instability at the linear level, which is eventually quenched due to the effect of non-linear terms. In this paper, we identify all of the terms in the Horndeski action that contribute to the (effective) mass term in the linearized equations and, hence, can cause or contribute to the tachyonic instability that triggers scalarization.
We study spontaneous scalarization of electrically charged extremal black holes in $D\geq 4$ 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 thermodynami…
We study static, spherically symmetric and electrically charged black hole solutions in a quadratic Einstein-scalar-Gauss-Bonnet gravity model. Very similar to the uncharged case, black holes undergo spontaneous scalarization for sufficiently large scalar-tensor coupling $γ$ - a phenomenon attributed to a tachyonic instability of the scalar field system. While in the uncharged case, this effect is only possible for positive values of $γ$, we show that for sufficiently large values of the electric charge $Q$ two independent domains of existence in the $γ$-$Q$-plane appear: one for positive $γ$ …
Extremal Scalarization of Charged Black Holes: Miransky Scaling across Reissner-Nordström Extremality
Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；Center for Quantum Spacetime, Sogang University（西江大学量子时空中心）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
We study scalarization of horizonless neutral compact reflecting stars. In our model, the scalar hair can be induced by the coupling of static scalar fields to the Gauss-Bonnet invariant. We analytically obtain lower bounds on the coupling parameter. Below the bound, the static scalar hair cannot form. And above the bound, we numerically get the discrete coupling parameter that can support scalar hairs outside stars. We also disclose effects of model parameters on the discrete coupling parameter.
We holographically investigate the scalarization in the Einstein-Scalar-Gauss-Bonnet gravity with a negative cosmological constant. We find that instability exists for both Schwarzschild-AdS and Reissner-Nordstrom-AdS black holes with planar horizons when we have proper interactions between the scalar field and the Gauss-Bonnet curvature corrections. We relate such instability to possible holographic scalarization and construct the corresponding hairy black hole solutions in the presence of the cosmological constant. Employing the holographic principle we expect that such bulk scalarization co…
In the present paper we consider a class of extended scalar-tensor-Gauss-Bonnet (ESTGB) theories for which the scalar degree of freedom is excited only in the extreme curvature regime. We show that in the mentioned class of ESTGB theories there exist new black hole solutions which are formed by spontaneous scalarization of the Schwarzaschild balck holes in the extreme curvature regime. In this regime, below certain mass, the Schwarzschild solution becomes unstable and new branch of solutions with nontrivial scalar field bifurcate from the Schwarzschild one. As a matter of fact, more than one b…
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 …
We construct black hole solutions with spin-induced scalarization in a class of models where a scalar field is quadratically coupled to the topological Gauss-Bonnet term. Starting from the tachyonically unstable Kerr solutions, we obtain families of scalarized black holes such that the scalar field has either even or odd parity, and we investigate their domain of existence. The scalarized black holes can violate the Kerr rotation bound. We identify "critical" families of scalarized black hole solutions such that the expansion of the metric functions and of the scalar field at the horizon no lo…
Even though black hole scalarization is extensively studied recently, little has been done in the direction of understanding the dynamics of this process, especially in the rapidly rotating regime. In the present paper, we focus exactly on this problem by considering the nonlinear dynamics of the scalar field while neglecting the backreaction on the spacetime metric. This approach has proven to give good results in various scenarios and we have explicitly demonstrated its accuracy for nonrotating black holes especially close to the bifurcation point. We have followed the evolution of a black h…
We study the spontaneous scalarization of spherically symmetric, static and asymptotically Anti-de Sitter (aAdS) black holes in a scalar-tensor gravity model with non-mininal coupling of the form $ϕ^2\left(α{\cal R} + γ{\cal G}\right)$, where $α$ and $γ$ are constants, while ${\cal R}$ and ${\cal G}$ are the Ricci scalar and Gauss-Bonnet term, respectively. Since these terms act as an effective ``mass'' for the scalar field, non-trivial values of the scalar field in the black hole space-time are possible for {\it a priori} vanishing scalar field mass. In particular, we demonstrate that the sca…
Chern-Simons gravity rotating Kerr-type black hole solutions are revisited from the point of view of their scalarization, namely examining the back reaction of pseudoscalar axion fields on the rotating geometry. To lowest order in an angular momentum expansion, and a long range approximation for both the axion field configuration and its back reaction onto the metric, such solutions had been discussed for the first time in the context of string theory. In this work, we extend the analysis to give analytic expressions for slowly rotating black holes outside the horizon, which formally include a…
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…
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…
Phase transitions in scalarized topological AdS black holes
Liaoning Key Laboratory of Cosmology and Astrophysics, College of Sciences, Northeastern University（东北大学理学院）；Center for Gravitation and Astrophysics, Kunming University of Science and Technology（昆明理工大学引力与天体物理中心）；Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics (Gansu) & Key Laboratory of Quantum Theory and Applications (MOE), Lanzhou University（兰州大学）；MOE Key Laboratory of Data Analytics and Optimization for Smart Industry, Northeastern University（东北大学）；National Frontiers Science Center for Industrial Intelligence and Systems Optimization, Northeastern University（东北大学）
It has recently been proved that nontrivial couplings between scalar fields and the Gauss-Bonnet invariant of a curved spacetime may allow a central black hole to support spatially regular scalar hairy configurations. Interestingly, former numerical studies of the intriguing black-hole spontaneous scalarization phenomenon have demonstrated that the composed hairy black-hole-scalar-field configurations exist if and only if the dimensionless coupling parameter $\barη$ of the theory belongs to a discrete set $\{[\barη^{-}_{n},\barη^{+}_{n}]\}_{n=0}^{n=\infty}$ of scalarization bands. We have exam…
In the multihorizon black hole spacetimes, it is possible that there are degenerate Cauchy horizons with vanishing surface gravities. We investigate the stability of the degenerate Cauchy horizon in black hole spacetimes. Despite the asymptotic behavior of spacetimes (flat, anti-de Sitter, or de Sitter), we find that the Cauchy horizon is stable against the classical perturbations, but unstable quantum mechanically.
