Spontaneous Scalarization Research Articles

Closing a spontaneous-scalarization window with binary pulsars

Benefitting from the unequaled precision of the pulsar timing technique, binary pulsars are important testbeds of gravity theories, providing some of the tightest bounds on alternative theories of gravity. One class of well-motivated alternative gravity theories, the scalar–tensor gravity, predict large deviations from general relativity for neutron stars through a nonperturbative phenomenon known as spontaneous scalarization. This effect, which cannot be tested in the Solar System, can now be tightly constrained using the latest results from the timing of a set of seven binary pulsars (PSRs J0348+0432, J1012+5307, J1738+0333, J1909−3744, J2222−0137, J0737−3039A, and J1913+1102), especially with the updated parameters of PSRs J2222−0137, J0737−3039A and J1913+1102. Using new timing results, we constrain the neutron star’s effective scalar coupling, which describes how strongly neutron stars couple to the scalar field, to a level of in a Bayesian analysis. Our analysis is thorough, in the sense that our results apply to all neutron star masses and all reasonable equations of state of dense matters, in the full relevant parameter space. It excludes the possibility of spontaneous scalarization of neutron stars, at least within a class of scalar–tensor gravity theories.

Nonequatorial scalar rings supported by magnetized Schwarzschild-Melvin black holes

It has recently been demonstrated that magnetized black holes in composed Einstein-Maxwell-scalar-Gauss-Bonnet field theories with a nonminimal negative coupling of the scalar field to the Gauss-Bonnet curvature invariant may support spatially regular scalar hairy configurations. In particular, it has been revealed that, for Schwarzschild-Melvin black-hole spacetimes, the onset of the near-horizon spontaneous scalarization phenomenon is marked by the numerically computed dimensionless critical relation $(BM{)}_{\mathrm{crit}}\ensuremath{\simeq}0.971$, where ${M,B}$ are respectively the mass and the magnetic field of the spacetime. In the present paper we prove, using analytical techniques, that the boundary between bald Schwarzschild-Melvin black-hole spacetimes and hairy (scalarized) black-hole solutions of the composed Einstein-Maxwell-scalar-Gauss-Bonnet theory is characterized by the exact dimensionless relation $(BM{)}_{\mathrm{crit}}=\sqrt{\frac{\sqrt{6}\ensuremath{-}2}{2\sqrt{6}}+\sqrt{\frac{\sqrt{6}\ensuremath{-}1}{2}}}$ for the critical magnetic strength. Intriguingly, we prove that the critical dimensionless magnetic parameter $(BM{)}_{\mathrm{crit}}$ corresponds to magnetized black holes that support a pair of linearized nonminimally coupled thin scalar rings that are characterized by the nonequatorial polar angular relation $({\mathrm{sin}}^{2}\ensuremath{\theta}{)}_{\mathrm{scalar}\ensuremath{-}\mathrm{ring}}=\frac{690\ensuremath{-}72\sqrt{6}+4\sqrt{3258\sqrt{6}\ensuremath{-}7158}}{789}<1$. It is also proved that the classically allowed angular region for the negative-coupling near-horizon spontaneous scalarization phenomenon of magnetized Schwarzschild-Melvin spacetimes is restricted to the black-hole poles, ${\mathrm{sin}}^{2}{\ensuremath{\theta}}_{\text{scalar}}\ensuremath{\rightarrow}0$, in the asymptotic large-strength magnetic regime $BM\ensuremath{\gg}1$.

Strong cosmic censorship in Einstein-Maxwell-Scalar-Gauss-Bonnet theory

Recently, it is found that the strong cosmic censorship (SCC) is violated in Reissner-Nordstrom-de Sitter (RNdS) black hole by a minimal coupled neutral massless scalar field at the linear perturbation level. For the Einstein-Maxwell-Scalar-Gauss-Bonnet theory, which is famous for the spontaneous scalarization phenomenon, there exists the scalar field coupled with the Gauss-Bonnet term. Whether the SCC of the RNdS black hole can be repaired by the nonminimal coupled scalar field perturbation at the linear level becomes an interesting question. In this paper, we first investigate the extendibility of the metric beyond the Cauchy horizon in the Einstein-Maxwell-Scalar-Gauss-Bonnet theory. Then, we examine the SCC of the RNdS black hole by calculating the quasinormal mode of the nonminimal coupled scalar field and find that the SCC can be recovered under some parameters.

Compact Objects in Alternative Gravities

We address neutron stars and black holes in alternative gravities, after recalling their basic properties in General Relativity. Among the plethora of interesting alternative gravities we here focus on an interesting set of scalar-tensor theories. We discuss the phenomenon of spontaneous scalarization, that is, matter induced for neutron stars and curvature induced for black holes. Along with other relevant physical properties, we address the quasi-normal modes of these compact objects. In particular, we consider universal relations of neutron stars to largely reduce the dependence on the equation of state, and we briefly address the shadow of black holes.

Beyond the spontaneous scalarization: New fully nonlinear mechanism for the formation of scalarized black holes and its dynamical development

In the present paper, we show the existence of a fully nonlinear mechanism for the formation of scalarized black holes, which is different from the spontaneous scalarization, and demonstrate its dynamical development. We consider a class of scalar-Gauss-Bonnet gravity theories within which no tachyonic instability can occur. Although the Schwarzschild black holes are linearly stable against scalar perturbations, we show dynamically that for certain choices of the coupling function, they are unstable against nonlinear scalar perturbations. This nonlinear instability leads to the formation of new black holes with scalar hair. The fully nonlinear and self-consistent study of the equilibrium black holes reveals that the spectrum of solutions is more complicated and more than one scalarized branch can exist. We have also considered classes of scalar-Gauss-Bonnet theories where both the standard and the nonlinear scalarization can be present, and they are smoothly connected that completes in an interesting way the picture of black hole scalarization. The fully nonlinear (de)scalarization of a Schwarzschild black hole will always happen with a jump because the stable ``scalarized branch'' is not continuously connected to the Schwarzschild one that can leave clear observational signatures.

Spin-induced black hole spontaneous scalarization: Analytic treatment in the large-coupling regime

It has recently been demonstrated numerically that spinning black holes whose dimensionless rotation parameter is larger than the critical value $(J/{M}^{2}{)}_{\mathrm{crit}}\ensuremath{\equiv}{\overline{a}}_{\mathrm{crit}}=\frac{1}{2}$ can support spatially regular hairy scalar configurations which are characterized by a nonminimal negative coupling to the Gauss-Bonnet curvature invariant. Motivated by this physically important observation, we explore, using analytical techniques, the physical and mathematical properties of the composed spinning-Kerr-black-hole-nonminimally-coupled-linearized-scalar-field configurations in the large-coupling $\ensuremath{-}\overline{\ensuremath{\eta}}\ensuremath{\gg}1$ regime (here $\overline{\ensuremath{\eta}}$ is the dimensionless coupling parameter of the composed black-hole-scalar-field theory). In particular, we derive a remarkably compact analytical formula for the spin-dependent critical existence line ${\overline{\ensuremath{\eta}}}_{\mathrm{crit}}={\overline{\ensuremath{\eta}}}_{\mathrm{crit}}(\overline{a})$ of the composed black-hole-field system. The physical significance of this critical line stems from the fact that, for a given value of the black-hole dimensionless rotation parameter $\overline{a}$, it marks the boundary between bald (scalarless) Kerr black holes and nonlinearly coupled hairy spinning-black-hole-scalar-field configurations.

Instability of vectorized stars

In recent papers it has been shown that a large class of vectorization mechanisms in gravity, which involve the vector fields becoming apparently tachyonic in some regime, are actually dominated by ghosts and non-perturbative behavior. Despite this, vectorized compact object solutions have previously been found, which raises the question of how, and if, the newly discovered ghosts are quenched in these cases. Here we develop the tools to study the perturbations of vectorized compact objects, and demonstrate that they suffer from ghosts and gradient instabilities as well. Thus, these vectorized objects do not represent the stable end point of a quenched instability unlike their scalarized counterparts in the spontaneous scalarization literature.

Ghost of vector fields in compact stars

Spontaneous scalarization is a mechanism that allows a scalar field to go undetected in weak gravity environments and yet develop a nontrivial configuration in strongly gravitating systems. At the perturbative level it manifests as a tachyonic instability around spacetimes that solve Einstein's equations. The endpoint of this instability is a nontrivial scalar field configuration that can significantly modify a compact object's structure and can produce observational signatures of the scalar field's presence. Does such a mechanism exists for vector fields? Here we revisit the model that constitutes the most straightforward generalization of the original scalarization model to a vector field and perform a perturbative analysis. We show that a ghost appears as soon as the square of the naive effective mass squared becomes negative anywhere. This result poses a serious obstacle in generalizing spontaneous scalarization to vector fields.

Neutron stars in massive scalar-Gauss-Bonnet gravity: Spherical structure and time-independent perturbations

The class of scalar-tensor theories with the scalar field coupling to the Gauss-Bonnet invariant has drawn great interest since solutions of spontaneous scalarization were found for black holes in these theories. We contribute to the existing literature a detailed study of the spontaneously scalarized neutron stars (NSs) in a typical theory where the coupling function of the scalar field takes the quadratic form and the scalar field is massive. The investigation here includes the spherical solutions of the NSs as well as their perturbative properties, namely the tidal deformability and the moment of inertia, treated in a unified and extendable way under the framework of spherical decomposition. We find that while the mass, the radius, and the moment of inertia of the spontaneously scalarized NSs show very moderate deviations from those of the NSs in general relativity (GR), the tidal deformability exhibits significant differences between the solutions in GR and the solutions of spontaneous scalarization for certain values of the parameters in the scalar-Gauss-Bonnet theory. As a result, the celebrated universal relation between the moment of inertia and the tidal deformability of neutron stars breaks down. With the mass and the tidal deformability of NSs attainable in the gravitational waves from binary NS mergers, the radius measurable using the X-ray satellites, and the moment of inertia accessible via the high-precision pulsar timing techniques, future multi-messenger observations can be contrasted with the theoretical results and provide us necessary information for building up theories beyond GR.

Neutron star scalarization with Gauss-Bonnet and Ricci scalar couplings

Spontaneous scalarization of neutron stars has been extensively studied in the Damour and Esposito-Far\`ese model, in which a scalar field couples to the Ricci scalar or, equivalently, to the trace of the energy-momentum tensor. However, scalarization of both black holes and neutron stars may also be triggered by a coupling of the scalar field to the Gauss-Bonnet invariant. The case of the Gauss-Bonnet coupling has also received a lot of attention lately, but the synergy of the Ricci and Gauss-Bonnet couplings has been overlooked for neutron stars. Here, we show that combining both couplings has interesting effects on the properties of scalarized neutron stars, such as affecting their domain of existence or the amount of scalar charge they carry.

Extended reduced-order surrogate models for scalar-tensor gravity in the strong field and applications to binary pulsars and gravitational waves

Statistically sound tests of scalar-tensor gravity theories in the strong-field regime usually involves computationally intensive calculations. In this study, we construct a reduced order surrogate model for the scalar-tensor gravity of Damour and Esposito-Far\`ese (DEF) with spontaneous scalarization phenomena developed for neutron stars (NSs). This model allows us to perform a rapid and comprehensive prediction of NS properties, including mass, radius, moment of inertia, effective scalar coupling, and two extra coupling parameters. We code the model in the pySTGROMX package, as an extension of our previous work, that speeds up the calculations at two and even three orders of magnitude and yet still keeps accuracy of $\sim1\%$. Using the model, we can calculate all the post-Keplerian parameters in the timing of binary pulsars conveniently, which provides a quick approach for us to place comprehensive constraints on the DEF theory. We perform Markov-chain Monte Carlo simulations with the model to constrain the parameters of the DEF theory with well-timed binary pulsars. Utilizing five NS-white dwarf and three NS-NS binaries, we obtain the most stringent constraints on the DEF theory up to now. Our work provides a public tool for quick evaluation of NSs' derived parameters to test gravity in the strong-field regime.

Scalar gravitational wave signals from core collapse in massive scalar–tensor gravity with triple-scalar interactions

The spontaneous scalarization during the stellar core collapse in the massive scalar–tensor theories of gravity introduces extra polarizations (on top of the plus and cross modes) in gravitational waves, whose amplitudes are determined by several model parameters. Observations of such scalarization-induced gravitational waveforms therefore offer valuable probes into these theories of gravity. Considering a triple-scalar interactions in such theories, we find that the self-coupling effects suppress the magnitude of the scalarization and thus reduce the amplitude of the associated gravitational wave signals. In addition, the self-interacting effects in the gravitational waveform are shown to be negligible due to the dispersion throughout the astrophysically distant propagation. As a consequence, the gravitational waves observed on the Earth feature the characteristic inverse-chirp pattern. Although not with the on-going ground-based detectors, we illustrate that the scalarization-induced gravitational waves may be detectable at a signal-to-noise ratio level of with future detectors, such as Einstein Telescope and Cosmic Explorer.

Scalarized neutron stars in massive scalar-tensor gravity: X-ray pulsars and tidal deformability

Neutron stars (NSs) in scalar-tensor theories of gravitation with the phenomenon of spontaneous scalarization can develop significant deviations from general relativity. Cases with a massless scalar have been studied widely. We compare the NS scalarizations in Damour--Esposito-Far\`ese theory, Mendes-Ortiz theory, and $\ensuremath{\xi}$ theory with a massive scalar field. Numerical solutions for slowly rotating NSs are obtained. They are used to construct the x-ray pulse profiles of a pair of extended hot spots on the surface of NSs. We also calculate the tidal deformability for NSs with spontaneous scalarization, which is done for the first time with a massive scalar field. We show the universal relation between the moment of inertia and the tidal deformability. The x-ray pulse profiles, the tidal deformability, and the universal relation may help us to constrain the massive scalar-tensor theories in x-ray and gravitational-wave observations of NSs, including the Neutron star Interior Composition Explorer satellite, the Square Kilometre Array telescope, and LIGO/Virgo/KAGRA laser interferometers.

Scalarized Einstein\u2013Maxwell-scalar black holes in a cavity

In this paper, we study the spontaneous scalarization of Reissner–Nordström (RN) black holes enclosed by a cavity in an Einstein–Maxwell-scalar (EMS) model with non-minimal couplings between the scalar and Maxwell fields. In this model, scalar-free RN black holes in a cavity may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. We calculate numerically the black hole solutions, and investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. The scalarized solutions are always thermodynamically preferred over RN black holes in a cavity. In addition, a reentrant phase transition, composed of a zeroth-order phase transition and a second-order one, occurs for large enough electric charge Q.

Dynamical charged black hole spontaneous scalarization in anti–de Sitter spacetimes

We study the fully nonlinear dynamics of the spherically symmetric black hole spontaneous scalarization in Einstein Maxwell scalar theory with coupling function $f(\ensuremath{\phi})={e}^{\ensuremath{-}b{\ensuremath{\phi}}^{2}}$, which can transform usual Reissner-Nordstr\"om 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 spherically symmetric hairy black hole provided that the constant $\ensuremath{-}b$ in the coupling function and the charge of the original black hole are sufficiently large, while the cosmological constant is small enough. In the scalarization process, we observe that the black hole irreducible mass initially increases exponentially, then it approaches to and finally saturates at a finite value. Choosing stronger coupling and larger black hole charge, we find that the black hole mass exponentially grows earlier and it takes longer time for a hairy black hole to be developed and stabilized. We further examine phase structure properties in the scalarization process and confirm the observations in the nonlinear dynamical study.

Spontaneous scalarization in scalar–tensor theories with conformal symmetry as an attractor

AbstractMotivated by constant-G theory, we introduce a one-parameter family of scalar–tensor theories as an extension of constant-G theory in which the conformal symmetry is a cosmological attractor. Since the model has the coupling function of negative curvature, we expect spontaneous scalarization to occur and that the parameter can be constrained by pulsar timing measurements. Modeling neutron stars with realistic equations of state, we study the structure of neutron stars and calculate the effective scalar coupling with the neutron star in these theories. We find that within the parameter region where the observational constraints are satisfied, the effective scalar coupling almost coincides with that derived using the quadratic model with the same curvature. This indicates that the constraints obtained by the quadratic model will be used to limit the curvature of the coupling function universally in the future.

Can supermassive black hole shadows test the Kerr metric?

The unprecedented image of the M87* supermassive black hole has sparked some controversy over its usefulness as a test of the general relativistic Kerr metric. The criticism is mainly related to the black hole's quasi-circular shadow and advocates that its radius depends not only on the black hole's true spacetime properties but also on the poorly known physics of the illuminating accretion flow. In this paper we take a sober view of the problem and argue that our ability to probe gravity with a black hole shadow is only partially impaired by the matter degrees of freedom and the number of non-Kerr parameters used in the model. As we show here, a more intriguing situation arises from the mass scaling of the dimensional coupling constants that typically appear in non-GR theories of gravity. Existing limits from gravitational wave observations imply that supermassive systems like the M87* black hole would suffer a suppression of all non-GR deviation parameters in their metric, making the spacetime and the produced shadow virtually Kerr. Therefore, a supermassive black hole shadow is likely to probe only those extensions of General Relativity which are endowed with dimensionless coupling constants or other special cases with a screening mechanism for black holes or certain types of spontaneous scalarisation.

Challenging cosmic censorship in Einstein-Maxwell-scalar theory with numerically simulated gedanken experiments

We perform extensive nonlinear numerical simulations of the spherical collapse of (charged) wavepackets onto a charged black hole within Einstein-Maxwell theory and in Einstein-Maxwell-scalar theory featuring nonminimal couplings and a spontaneous scalarization mechanism. We confirm that black holes in full-fledged Einstein-Maxwell theory cannot be overcharged past extremality and no naked singularities form, in agreement with the cosmic censorship conjecture. We show that naked singularities do not form even in Einstein-Maxwell-scalar theory, although it is possible to form scalarized black holes with charge above the Reissner-Nordstr\"om bound. We argue that charge and mass extraction due to superradiance at fully nonlinear level is crucial to bound the charge-to-mass ratio of the final black hole below extremality. We also discuss some "descalarization" mechanisms for scalarized black holes induced either by superradiance or by absorption of an opposite-charged wavepacket; in all cases the final state after descalarization is a subextremal Reissner-Nordstr\"om black hole.

Dynamical Formation of Scalarized Black Holes and Neutron Stars through Stellar Core Collapse.

In a certain class of scalar-Gauss-Bonnet gravity, the black holes and the neutron stars can undergo spontaneous scalarization-a strong gravity phase transition triggered by a tachyonic instability due to the nonminimal coupling between the scalar field and the spacetime curvature. Studies of this phenomenon have, so far, been restricted mainly to the study of the tachyonic instability and stationary scalarized black holes and neutron stars. To date, no realistic physical mechanism for the formation of isolated scalarized black holes and neutron stars has been proposed. We study, for the first time, the spherically symmetric fully nonlinear stellar core collapse to a black hole and a neutron star in scalar-Gauss-Bonnet theories allowing for a spontaneous scalarization. We show that the core collapse can produce scalarized black holes and scalarized neutron stars starting with a nonscalarized progenitor star. The possible paths to reach the end (non)scalarized state are quite rich leading to interesting possibilities for observational manifestations.

Scalarized Einstein\u2013Maxwell-scalar black holes in anti-de Sitter spacetime

In this paper, we study spontaneous scalarization of asymptotically anti-de Sitter charged black holes in an Einstein–Maxwell-scalar model with a non-minimal coupling between the scalar and Maxwell fields. In this model, Reissner–Nordström-AdS (RNAdS) black holes are scalar-free black hole solutions, and may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. For RNAdS and scalarized black hole solutions, we investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. In a micro-canonical ensemble, scalarized solutions are always thermodynamically preferred over RNAdS black holes. However, the system has much richer phase structure and phase transitions in a canonical ensemble. In particular, we report a RNAdS BH/scalarized BH/RNAdS BH reentrant phase transition, which is composed of a zeroth-order phase transition and a second-order one.