Spontaneous Scalarization Research Articles

Slowly rotating black holes and their scalarization

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 scalar mode. A threshold (existence) curve is obtained from the constant scalar modes under time evolution, which means the boundary between stable and unstable black holes. It is found that the slowly rotating black holes turn out to be unstable against a spherically symmetric scalar-mode propagation for positive coupling $\alpha$. However, we could not find tachyonic instability and any $a$-bound for scalarization for negative coupling $\alpha$.

Dynamics of Spontaneous Black Hole Scalarization and Mergers in Einstein-Scalar-Gauss-Bonnet Gravity.

We study the dynamics of black holes in scalar Einstein-Gauss-Bonnet theories that exhibit spontaneous black hole scalarization using recently introduced methods for solving the full, nonperturbative equations of motion. For one sign of the coupling parameter, nonspinning 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 saturates in a scalarized black hole that is stable without symmetry assumptions. However, this parameter space range is significantly smaller than the range for which stationary scalarized black hole solutions exist. We show how different choices for the subleading behavior of the Gauss-Bonnet coupling affect the dynamics of the instability and the final state, or lack thereof. Finally, we present mergers of binary black holes and demonstrate the imprint of the scalar hair in the gravitational radiation.

Horizon curvature and spacetime structure influences on black hole scalarization

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.

Neutron stars in scalar-tensor theories: Analytic scalar charges and universal relations

Neutron stars are ideal astrophysical sources to probe general relativity due to their large compactnesses and strong gravitational fields. For example, binary pulsar and gravitational wave observations have placed stringent bounds on certain scalar-tensor theories in which a massless scalar field is coupled to the metric through matter. A remarkable phenomenon of neutron stars in such scalar-tensor theories is spontaneous scalarization, where a normalized scalar charge remains order unity even if the matter-scalar coupling vanishes asymptotically far from the neutron star. While most works on scalarization of neutron stars focus on numerical analysis, this paper aims to derive accurate scalar charges analytically. To achieve this, we consider a simple energy density profile of the Tolman VII form and work in a weak-field expansion. We solve the modified Tolman-Oppenheimer-Volkoff equations order by order and apply Pad\'e resummation to account for higher-order effects. We find that our analytic scalar charges in terms of the stellar compactness beautifully model those computed numerically. We also find a quasi-universal relation between the scalar charge and stellar binding energy that is insensitive to the underlying equations of state. Comparison of analytic scalar charges for Tolman VII and constant density stars mathematically support this quasi-universal relation. The analytic results found here provide physically motivated, ready-to-use accurate expressions for scalar charges.

Black hole scalarization with Gauss-Bonnet and Ricci scalar couplings

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.

Dynamical Descalarization in Binary Black Hole Mergers.

Scalar fields coupled to the Gauss-Bonnet invariant can undergo a tachyonic instability, leading to spontaneous scalarization of black holes. Studies of this effect have so far been restricted to single black hole spacetimes. We present the first results on dynamical scalarization in head-on collisions and quasicircular inspirals of black hole binaries with numerical relativity simulations. We show that black hole binaries can either form a scalarized remnant or dynamically descalarize by shedding off its initial scalar hair. The observational implications of these findings are discussed.

Scalarization of slowly rotating black holes

It is interesting to note that most black holes are born very slowly rotating. We investigate scalarization of slowly rotating black holes in the Einstein-scalar-Chern–Simons (EsCS) theory. In the slow rotation approximation, the CS term takes a linear form of rotation parameter [Formula: see text] which determines the tachyonic instability. The tachyonic instability for slowly rotating black holes represents the onset of spontaneous scalarization. It is shown that the slowly rotating black holes are unstable against a spherically symmetric scalar-mode perturbation for positive coupling [Formula: see text], whereas these black holes are unstable for negative coupling without any [Formula: see text]-bound.

Spontaneous scalarization of charged stars

We study static and spherically symmetric charged stars with a nontrivial profile of the scalar field ϕ in Einstein-Maxwell-scalar theories. The scalar field is coupled to a U(1) gauge field Aμ with the form −α(ϕ)FμνFμν/4, where Fμν=∂μAν−∂νAμ is the field strength tensor. Analogous to the case of charged black holes, we show that this type of interaction can induce spontaneous scalarization of charged stars under the conditions (dα/dϕ)(0)=0 and (d2α/dϕ2)(0)>0. For the coupling α(ϕ)=exp⁡(−βϕ2/Mpl2), where β(<0) is a coupling constant and Mpl is a reduced Planck mass, there is a branch of charged star solutions with a nontrivial profile of ϕ approaching 0 toward spatial infinity, besides a branch of general relativistic solutions with a vanishing scalar field, i.e., solutions in the Einstein-Maxwell model. As the ratio ρc/ρm between charge density ρc and matter density ρm increases toward its maximum value, the mass M of charged stars in general relativity tends to be enhanced due to the increase of repulsive Coulomb force against gravity. In this regime, the appearance of nontrivial branches induced by negative β of order −1 effectively reduces the Coulomb force for a wide range of central matter densities, leading to charged stars with smaller masses and radii in comparison to those in the general relativistic branch. Our analysis indicates that spontaneous scalarization of stars can be induced not only by the coupling to curvature invariants but also by the scalar-gauge coupling in Einstein gravity.

Scalarization-like mechanism through spacetime anisotropic scaling symmetry

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 $z\ensuremath{\ge}1$. 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 first law is satisfied and providing the corresponding Smarr formula, both of these relations account for an electric contribution. Furthermore, we show that for a certain parameter region, the anisotropic field configuration with a nonzero scalar field is thermodynamically preferred. This observation, together with a direct verification of the so-called scalarization conditions, suggest that the emergence of the dilaton field is due to a mechanism similar to spontaneous scalarization.

Spontaneous scalarization of self-gravitating magnetic fields

In this paper, we study the spontaneous scalarization of an extended, self-gravitating system which is static, cylindrically symmetric and possesses electromagnetic fields. We demonstrate that a real massive scalar field condenses on this Melvin magnetic universe solution when introducing a nonminimal coupling between the scalar field and (a) the magnetic field and (b) the curvature of the space-time, respectively. We find that in both cases, the solutions exist on a finite interval of the coupling constant and that solutions with a number of nodes $k$ in the scalar field are present. For case (a) we observe that the intervals of existence are mutually exclusive for different $k$.

Scalarized Einstein-Born-Infeld black holes

The phenomenon of spontaneous scalarization of Reissner-Nordstr\"{o}m (RN) black holes has recently been found in an Einstein-Maxwell-scalar (EMS) model due to a non-minimal coupling between the scalar and Maxwell fields. Non-linear electrodynamics, e.g., Born-Infeld (BI) electrodynamics, generalizes Maxwell's theory in the strong field regime. Non-minimally coupling the BI field to the scalar field, we study spontaneous scalarization of an Einstein-Born-Infeld-scalar (EBIS) model in this paper. It shows that there are two types of scalarized black hole solutions, i.e., scalarized RN-like and Schwarzschild-like solutions. Although the behavior of scalarized RN-like solutions in the EBIS model is quite similar to that of scalarize solutions in the EMS model, we find that there exist significant differences between scalarized Schwarzschild-like solutions in the EBIS model and scalarized solutions in the EMS model. In particular, the domain of existence of scalarized Schwarzschild-like solutions possesses a certain region, which is composed of two branches. The branch of larger horizon area is a family of disconnected scalarized solutions, which do not bifurcate from scalar-free black holes. However, the branch of smaller horizon area may or may not bifurcate from scalar-free black holes depending on the parameters. Additionally, these two branches of scalarized solutions can be both entropically disfavored over comparable scalar-free black holes in some parameter region.

Thin accretion disk signatures of scalarized black holes in Einstein-scalar-Gauss-Bonnet gravity

Einstein-scalar-Gauss-Bonnet gravity has recently been known to exhibit spontaneous scalarization. In the presence of the Gauss-Bonnet term the no-hair theorem can be evaded and novel black hole solutions with non-trivial scalar fields have been found besides the general relativistic solutions. In this paper, we aim to investigate the possibility of observationally testing Einstein-scalar-Gauss-Bonnet gravity using thin accretion disk properties around such scalarized black holes. Using the Novikov-Thorne model, we numerically calculate the electromagnetic flux, temperature distribution, emission spectrum, innermost stable circular orbits and energy conversion efficiency of accretion disks around such black holes and compare the results with the standard general relativistic Schwarzschild solution. We find that the accretion disks around scalarized black holes are hotter and more luminous than in general relativity.

Spontaneous scalarization of a conducting sphere in Maxwell-scalar models

We study the spontaneous scalarization of a standard conducting charged sphere embedded in Maxwell-scalar models in flat spacetime, wherein the scalar field $\phi$ 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{exactly} linearizes the scalar field equation, and the remaining two that produce nonlinear continuations of the first one. We show that the former model leads to a runaway behaviour in regions of the parameter space and neither the Coulomb nor the scalarized solutions are stable in the model; but the latter models can heal this behaviour producing stable scalarized solutions that are dynamically preferred over the Coulomb one. This parallels reports on black hole scalarization in the extended-scalar-Gauss-Bonnet models. Moreover, we analyse the impact of the choice of the boundary conditions on the scalarization phenomenon. Dirichlet and Neumann boundary conditions accommodate both (linearly) stable and unstable parameter space regions, for the scalar-free conducting sphere; but radiative boundary conditions always yield an unstable scalar-free solution and preference for scalarization. Finally, we perform numerical evolution of the full Maxwell-scalar system, following dynamically the scalarization process. They confirm the linear stability analysis and reveal that the scalarization phenomenon can occur in qualitatively distinct ways.

Constraining unmodeled physics with compact binary mergers from GWTC-1

We present a flexible model to describe the effects of generic deviations of observed gravitational-wave signals from modeled waveforms in the LIGO and Virgo gravitational-wave detectors. With the detection of 11 gravitational-wave events from the GWTC-1 catalog, we are able to constrain possible deviations from our modeled waveforms. In this paper, we present our coherent spline model that describes the deviations, then choose to validate our model on an example phenomenological and astrophysically motivated departure in waveforms based on extreme spontaneous scalarization. We find that the model is capable of recovering the simulated deviations. By performing model comparisons, we observe that the spline model effectively describes the simulated departures better than a normal compact binary coalescence (CBC) model. We analyze the entire GWTC-1 catalog of events with our model and compare it to a normal CBC model, finding that there are no significant departures from the modeled template gravitational waveforms used.

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.

Scalar-connection gravity and spontaneous scalarization

Scalar-tensor theories of gravity are known to allow significant deviations from general relativity through various astrophysical phenomena. In this paper, we formulate a scalar-connection gravity by setting up scalars and connection configurations instead of metric. Since the matter sector is not straightforward to conceive without a metric, we invoke cosmological fluids in terms of their one-form velocity in the volume element of the invariant action. This leads to gravitational equations with a perfect fluid source and a generated metric, which are expected to produce reasonable deviations from general relativity in the strong field regime. As a relevant application, we study a spontaneous scalarization mechanism and show that the Damour-Esposito-Far\`ese model arises in a certain class of scalar-connection gravity. Furthermore, we investigate a general study in which the present framework becomes distinguishable from the famed scalar-tensor theories.

Compact object scalarization with general relativity as a cosmic attractor

We demonstrate that there are theories that exhibit spontaneous scalarization in the strong gravity regime while having General Relativity with a constant scalar as a cosmological attractor. We identify the minimal model that has this property and discuss its extensions.

Spin-Induced Scalarized Black Holes.

It was recently shown that a scalar field suitably coupled to the Gauss-Bonnet invariant G can undergo a spin-induced linear tachyonic instability near a Kerr black hole. This instability appears only once the dimensionless spin j is sufficiently large, that is, j≳0.5. A tachyonic instability is the hallmark of spontaneous scalarization. Focusing, for illustrative purposes, on a class of theories that do exhibit this instability, we show that stationary, rotating black hole solutions do indeed have scalar hair once the spin-induced instability threshold is exceeded, while black holes that lie below the threshold are described by the Kerr solution. Our results provide strong support for spin-induced black hole scalarization.

Magnetic deformation of neutron stars in scalar-tensor theories

Scalar-tensor theories are among the most promising alternatives to general relativity that have been developed to account for some long-standing issues in our understanding of gravity. Some of these theories predict the existence of a non-linear phenomenon that is spontaneous scalarisation, which can lead to the appearance of sizable modifications to general relativity in the presence of compact matter distributions, namely neutron stars. On the one hand, one of the effects of the scalar field is to modify the emission of gravitational waves that are due to both variations in the quadrupolar deformation of the star and the presence of additional modes of emission. On the other hand, neutron stars are known to harbour extremely powerful magnetic fields which can affect their structure and shape, leading, in turn, to the emission of gravitational waves – in this case due to a magnetic quadrupolar deformation. In this work, we investigate how the presence of spontaneous scalarisation can affect the magnetic deformation of neutron stars and their emission of quadrupolar gravitational waves, both of tensor and scalar nature. We show that it is possible to provide simple parametrisations of the magnetic deformation and gravitational wave power of neutron stars in terms of their baryonic mass, circumferential radius, and scalar charge, while also demonstrating that a universal scaling exists independently of the magnetic field geometry and of the parameters of the scalar-tensor theory. Finally, we comment on the observability of the deviations in the strain of gravitational waves from general relativity by current and future observatories.

Spin-Induced Black Hole Spontaneous Scalarization

We study scalar fields in a black hole background and show that, when the scalar is suitably coupled to curvature, rapid rotation can induce a tachyonic instability. This instability, which is the hallmark of spontaneous scalarization in the linearized regime, is expected to be quenched by nonlinearities and endow the black hole with scalar hair. Hence, our results demonstrate the existence of a broad class of theories that share the same stationary black hole solutions with general relativity at low spins, but which exhibit black hole hair at sufficiently high spins (a/M≳0.5). This result has clear implications for tests of general relativity and the nature of black holes with gravitational and electromagnetic observations.