Spontaneous scalarization is a gravitational phenomenon in which deviations from general relativity arise once a certain threshold in curvature is exceeded, while being entirely absent below that threshold. For black holes, scalarization is known to be triggered by a coupling between a scalar and the Gauss-Bonnet invariant. A coupling with the Ricci scalar, which can trigger scalarization in neutron stars, is instead known to not contribute to the onset of black hole scalarization, and has so far been largely ignored in the literature when studying scalarized black holes. In this paper, we study the combined effect of both these couplings on black hole scalarization. We show that the Ricci coupling plays a significant role in the properties of scalarized solutions and their domain of existence. This work is an important step in the construction of scalarization models that evade binary pulsar constraints and have general relativity as a cosmological late-time attractor, while still predicting deviations from general relativity in black hole observations.
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…
We study the dynamics of black holes in Einstein-scalar-Gauss-Bonnet theories that exhibit spontaneous black hole scalarization using recently introduced methods for solving the full, non-perturbative equations of motion. For one sign of the coupling parameter, non-spinning vacuum black holes are unstable to developing scalar hair, while for the other, instability only sets in for black holes with sufficiently large spin. We study scalarization in both cases, demonstrating that there is a range of parameter space where the theory maintains hyperbolic evolution and for which the instability sat…
We identify a class of scalar-tensor theories with coupling between the scalar and the Gauss-Bonnet invariant that exhibit spontaneous scalarization for both black holes and compact stars. In particular, these theories formally admit all of the stationary solutions of general relativity, but these are not dynamically preferred if certain conditions are satisfied. Remarkably, black holes exhibit scalarization if their mass lies within one of many narrow bands. We find evidence that scalarization can occur in neutron stars as well.
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.
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 im…
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…
For massless scalar fields, a relation $Δ_{n}=\frac{\sqrt{3}}{2}π$ for $n\rightarrow \infty$ was observed in the scalar-Gauss-Bonnet theory. In the present paper, we extend the discussion by including a nonzero scalar field mass. For massive scalar fields, we show that the relation $Δ_{n}=\frac{\sqrt{3}}{2}π$ for $n\rightarrow \infty$ still holds. We demonstrate this relation with both analytical and numerical methods. The analytical analysis implies that this relation may be a very universal behavior.
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 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…
We study the perturbative behaviour of topological black holes in the presence of a cosmological constant and a scalar field coupled to the Gauss-Bonnet term. We calculate both analytically and numerically the quasi-normal modes of scalar perturbations in the extended scalar-tensor-Gauss-Bonnet gravity. In the case of small black holes we find a phase transition of the topological black hole to a hairy configuration.
In a subclass of scalar-tensor theories, it has been shown that standard general relativity solutions of neutron stars and black holes with trivial scalar field profiles are unstable. Such an instability leads to solutions which are different from those of general relativity and have non-trivial scalar field profiles, in a process called scalarization. In the present work we focus on scalarization due to a non-minimal coupling of the scalar field to the Gauss-Bonnet curvature invariant. The coupling acts as a tachyonic mass for the scalar mode, thus leading to the instability of general relati…
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…
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 quest…
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…
With certain non-minimal 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 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 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 metho…
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 Schwarzschild black hole is linearly stable but instead nonlinear instability can kick-in. In the present paper we extend on this idea in the case of multi-scalar 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 …
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…
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…
Recently, by considering nontrivial couplings between scalar fields and the Gauss-Bonnet invariant, the Schwarzschild black hole may allow regular scalar hairy configurations. The numerical studies of this spontaneous scalarization phenomenon show if the coupling parameter $\barη$ belongs to discrete sets $\barη\in\{\barη^-_n,\barη^+_n\}^{n=\infty}_{n=0}$, the black hole can support regular scalar hairy configurations. Interestingly, Hod finds the coupling parameter $\barη^+_n$ which correspond to the black hole linearized scalar field configurations has an asymptotic universal behavior $Δ_n\e…
In the presence of appropriate non-minimal couplings between a scalar field and the curvature squared Gauss-Bonnet (GB) term, compact objects such as neutron stars and black holes (BHs) can spontaneously scalarize, becoming a preferred vacuum. Such strong gravity phase transitions have attracted considerable attention recently. The non-minimal coupling functions that allow this mechanism are, however, always postulated ad hoc. Here we point out that families of such functions naturally emerge in the context of Higgs--Chern-Simons gravity models, which are found as dimensionally descents of hig…
Phase Structure of Scalarized Black Holes in Einstein-Scalar-Gauss-Bonnet Gravity
Universidade de Aveiro（阿威罗大学）；Centre for Research and Development in Mathematics and Applications (CIDMA)（数学与应用研究中心（CIDMA））；UFPA（帕拉联邦大学）；Jiangxi Normal University（江西师范大学）；Universität Oldenburg（奥尔登堡大学）
In the present paper we derive strong constrains on scalarization in scalar-Gauss-Bonnet (sGB) gravity using observations of pulsars in close binary systems. Since scalarized neutron stars carry a nonzero scalar change, they emit scalar dipole radiation while inspiraling which speeds up the orbital decay. The observations support the conjecture that such radiation is either absent or very small for the observed binary pulsars. Using this, we determine the allowed range of parameters for sGB gravity. We also transfer the derived constraints to black holes in sGB gravity. It turns out that the m…
The scalarization is a very interesting phenomena allowing to endow a compact object with scalar hair while leaving all the predictions in the weak field limit unaltered. In Gauss-Bonnet gravity the source of the scalar field can be the curvature of the space-time. It was recently shown that for a particular type of coupling function between the scalar field and the Gauss-Bonnet invariant, spin-induced black hole scalarization is possible. In the present paper we study this phenomenon by performing a 2+1 time evolution of the relevant linearized scalar field perturbation equation and examine t…
In general relativity, astrophysical black holes are simple objects, being described by just their mass and spin. These simple solutions are not exclusive to general relativity, as they also appear in theories that allow for an extra scalar degree of freedom. Recently, it was shown that some theories which couple a scalar field with the Gauss-Bonnet invariant can have the same classic general relativity black hole solutions as well as hairy black holes. These scalarized solutions can be stable, having an additional "charge" term that has an impact on the gravitational-wave emission by black ho…
Recently new scalarized black hole solutions were constructed in the extended scalar-tensor-Gauss-Bonnet gravity, where the scalar field is sourced by the curvature of the spacetime via the Gauss-Bonnet invariant. A natural extension of these results is to consider the case of nonzero black hole charge. In addition we have explored a large set of coupling functions between the Gauss-Bonnet invariant and the scalar field, that was not done until now even in the uncharged case, in order to understand better the behavior of the solutions and the deviations from pure general relativity. The result…
In the present paper we study the onset of the spin-induced scalarization of a Kerr black hole in scalar-Gauss-Bonnet gravity with a massive scalar field. Our approach is based on a (2+1) time evolution of the relevant linearized scalar field perturbation equation. We examine the region where the Kerr black hole becomes unstable giving rise to new scalarized rotating black holes with a massive scalar field. With increasing of the scalar field mass, the minimum value of the Gauss-Bonnet coupling parameter at which scalarization is possible, increases and thus the instability region shrinks. Int…
Proofs on singularity-free solutions and scalarization in nonlinear Einstein-scalar-Gauss-Bonnet cosmology
School of Mathematics and Statistics, Huazhong University of Science and Technology（华中科技大学数学与统计学院）；Center for Mathematical Sciences and School of Mathematics and Statistics, Huazhong University of Science and Technology（华中科技大学数学科学中心及数学与统计学院）；School of Mathematical Sciences, Xiamen University（厦门大学数学科学学院）
In the present paper we consider multi-scalar extension of Einstein-Gauss-Bonnet gravity. We focus on multi-scalar Einstein-Gauss-Bonnet models whose target space is a three-dimensional maximally symmetric space, namely either $\mathbb{S}^3$, $\mathbb{H}^3$ or $\mathbb{R}^3$, and in the case when the map $\text{\it spacetime} \to \text{\it target space}$ is nontrivial. We prove numerically the existence of black holes in this class of models for several Gauss-Bonnet coupling functions, including the case of scalarization. We also perform systematic study of a variety of black hole characterist…
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 $λ$ 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$\,\unicode{x2014}\,$whose primary black hole has a spin that is bounde…
It has recently been shown that nontrivial couplings between a scalar and the Gauss-Bonnet invariant can give rise to black hole spontaneous scalarization. Theories that exhibit this phenomenon are among the leading candidates for testing gravity with upcoming black hole observations. All models considered so far have focused on specific forms for the coupling, neglecting scalar self-interactions. In this work, we take the first steps towards placing this phenomenon on a more robust theoretical footing by considering the leading-order scalar self-interactions as well as the scalar-Gauss-Bonnet…
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…
It is well-known that there exists a Hawking-Page phase transition between a spherical AdS black hole and a thermal AdS space. The phase transition does not happen between a Ricci flat AdS black hole whose horizon is a Ricci flat space and a thermal AdS space in the Poincare coordinates. However, the Hawking-Page phase transition occurs between a Ricci flat AdS black hole and an AdS soliton if at least one of horizon coordinates for the Ricci flat black hole is compact. We show a similar phase transition betwen the Ricci flat black holes and deformed AdS solitons in the Gauss-Bonnet gravity an…
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…
We study scalarization of slowly rotating black holes in the Einstein-scalar-Gauss-Bonnet (GB)-Chern-Simons (CS) theory. In the slow rotation approximation of $a\ll1$ with rotation parameter $a$, the GB term is given by a term for Schwarzschild black hole, whereas the CS term takes a linear term of $a$. The tachyonic instability for slowly rotating black holes represents the onset of spontaneous scalarization. We use the (2+1)-dimensional hyperboloidal foliation method to show the tachyonic instability for slowly rotating black holes by considering the time evolution of a spherically symmetric…
We investigate the Ricci Dark Energy (RDE) in the braneworld models with a Gauss-Bonnet term in the Bulk. We solve the generalized Friedmann equation on the brane analytically and find that the universe will finally enter into a pure de Sitter spacetime in stead of the big rip that appears in the usual 4D Ricci dark energy model with parameter $α<1/2$. We also consider the Hubble horizon as the IR cutoff in holographic dark energy model and find it can not accelerate the universe as in the usual case without interacting.
