We perform the stability analysis of the Kerr black hole in the Einstein-Chern-Simons-Scalar theory with quadratic scalar coupling. For positive coupling parameter ($α>0$), we introduce the (2+1)-dimensional hyperboloidal foliation method to show that the Kerr black hole is unstable against scalar-mode perturbation. In case of $α<0$, it is shown that the Kerr black hole is unstable without any $α$-independent bound on the rotation parameter $a$ when using the the hyperboloidal foliation method. The disappearance of the $a$-bound is confirmed analytically by implementing the (1+1)-dimensional linearized scalar equation.
We construct scalarized wormholes with a NUT charge in higher curvature theories. We consider both Einstein-scalar-Gauss-Bonnet and Einstein-scalar-Chern-Simons theories, following a recent paper by Brihaye et al. [1], where spontaneously scalarised Schwarzschild-NUT solutions were studied. By varying the coupling parameter and the scalar charge we determine the domain of existence of the scalarized nutty wormholes, and their dependence on the NUT charge. In the Gauss-Bonnet case the known set of scalarized wormholes [2] is reached in the limit of vanishing NUT charge. In the Chern-Simons case…
In the present paper, we construct spontaneously scalarized rotating black hole solutions in dynamical Chern-Simons (dCS) gravity by following the scalar field evolution in the decoupling limit. For the range of parameters where the Kerr black hole becomes unstable within dCS gravity the scalar field grows exponentially until it reaches an equilibrium configuration that is independent of the initial perturbation. Interestingly, the $\mathbb{Z}_2$ symmetry of the scalar field is broken and a strong maximum around only one of the rotational axes can be observed. The black hole scalar charge is c…
We carry out the stability analysis of the Schwarzschild black hole in Gauss-Bonnet and Chern-Simons-scalar theory. Here, we introduce two quadratic scalar couplings ($ϕ_1^2,ϕ_2^2$) to Gauss-Bonnet and Chern-Simons terms, where the former term is parity-even, while the latter one is parity-odd. The perturbation equation for the scalar $ϕ_1$ is the Klein-Gordon equation with an effective mass, while the perturbation equation for $ϕ_2$ is coupled to the parity-odd metric perturbation, providing a system of two coupled equations. It turns out that the Schwarzschild black hole is unstable against …
The tachyonic instability of the Kerr black holes is analyzed in the Einstein-scalar theory with the quadratic scalar couplings to two topological terms which are parity-even Gauss-Bonnet and parity-odd Chern-Simons terms. For positive coupling $α$, we use the (2+1)-dimensional hyperboloidal foliation method to derive the threshold curve which is the boundary between stable and unstable Kerr black holes by considering a spherically symmetric scalar-mode perturbation. In case of negative coupling, a newly bound of $a\ge0.26$ with $a$ the rotation parameter is found for unstable Kerr black holes…
We investigate scalarized charged black holes in the Einstein-Maxwell-Scalar theory with two U(1) fields inspired by the $N=4$ supergravity. From the onset of the spontaneous scalarization (tachyonic instability of Reissner-Nordström black hole), these black holes are classified by the number of $n=0,1,2,\cdots$, where $n=0$ is called the fundamental black hole and $n=1,2,\cdots$ denote the $n$-excited black holes. Adopting radial perturbations, we show that the $n=0$ black hole is stable against the $s(l=0)$-mode scalar perturbation, whereas the $n=1,2$ excited black holes are unstable. This …
We study the scalar perturbation on the background of a Kerr black hole in the dynamical Chern-Simons modified gravity with a quadratic coupling between the scalar field and Chern-Simons term. In particular, the late-time tails of scalar perturbations are investigated numerically in time domain by using the hyperboloidal foliation method. It is found that the Kerr black hole becomes unstable under linear perturbations in a certain region of the parameter space, which depends on the harmonic azimuthal index $m$ of the perturbation's mode. This may indicate that some Kerr black holes in this the…
Scalar-tensor theories of gravity where a new scalar degree of freedom couples to the Gauss-Bonnet invariant can exhibit the phenomenon of spontaneous black hole scalarization. These theories admit both the classic black holes predicted by general relativity as well as novel hairy black hole solutions. The stability of the hairy black holes is strongly dependent on the precise form of the scalar-gravity coupling. A radial stability investigation revealed that all scalarized black hole solutions are unstable when the coupling between the scalar field and the Gauss-Bonnet invariant is quadratic …
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…
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 stu…
Transgression Completion for Chern-Simons Black Hole Thermodynamics
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Institute of Fundamental Physics and Quantum Technology, Ningbo University（宁波大学基础物理与量子技术学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学科学学院，中国科学院大学）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
We study massive scalar field perturbation on Kerr black holes in dynamical Chern-Simons gravity by performing a $(2+1)$-dimensional simulation. Object pictures of the wave dynamics in time domain are obtained. The tachyonic instability is found to always occur for any nonzero black hole spin and any scalar field mass as long as the coupling constant exceeds a critical value. The presence of the mass term suppresses or even quenches the instability. The quantitative dependence of the onset of the tachyonic instability on the coupling constant, the scalar field mass and the black hole spin is g…
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…
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 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…
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…
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 $a$ 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 $α$, whereas these bla…
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…
It has recently been demonstrated that black holes with spatially regular horizons can support external scalar fields (scalar hairy configurations) which are non-minimally coupled to the Gauss-Bonnet invariant of the curved spacetime. The composed black-hole-scalar-field system is characterized by a critical existence line $α=α(μr_{\text{H}})$ which, for a given mass of the supported scalar field, marks the threshold for the onset of the spontaneous scalarization phenomenon [here $\{α,μ,r_{\text{H}}\}$ are respectively the dimensionless non-minimal coupling parameter of the field theory, the p…
We carry out numerical-relativity simulations of coalescing binary neutron stars in a scalar-tensor theory that admits spontaneous scalarization. We model neutron stars with realistic equations of state. We choose the free parameters of the theory taking into account the constraints imposed by the latest observations of neutron-star-- white-dwarf binaries with pulsar timing. We show that even within those severe constraints, scalarization can still affect the evolution of the binary neutron stars not only during the late inspiral, but also during the merger stage. We also confirm that even whe…
Spin-charge induced scalarization of Kerr-Newman black holes in the Einstein-Maxwell-scalar theory with scalar potential
College of Physics and Communication Electronics, Jiangxi Normal University（江西师范大学物理与通信电子学院）；Center for Quantum Spacetime, Sogang University（西江大学量子时空中心）
Although general relativity passes all precision tests to date, there are several reasons to go beyond the current model of gravitation and search for new fundamental physics. This means looking for new, so far undetected, fields. Scalars are the easiest fields to consider and they are ubiquitous in both extensions of the Standard Model and in alternative theories of gravity. That is why a lot of attention has been drawn towards the investigation of scalar-tensor theories, where gravity is described by both the metric tensor and a scalar field. A particularly interesting phenomenon that has re…
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…
It has recently been demonstrated that magnetized black holes in composed Einstein-Maxwell-scalar-Gauss-Bonnet field theories with a non-minimal 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 $(BM)_{\text{crit}}\simeq0.971$, where $\{M,B\}$ are respectively the mass and the magnetic…
