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Register a new userSpontaneous scalarization of charged black holes at the approach to extremality
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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 $gamma$ - 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 $gamma$, we show that for sufficiently large values of the electric charge $Q$ two independent domains of existence in the $gamma$-$Q$-plane appear: one for positive $gamma$ and one for negative $gamma$. We demonstrate that this new domain for negative $gamma$ exists because of the fact that the near-horizon geometry of a nearly extremally charged black hole is $AdS_2times S^2$.This new domain appears for electric charges larger than approximately 74$%$ of the extremal charge. For positive $gamma$ we observe that a singularity with diverging curvature invariants forms outside the horizon when approaching extremality.
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We present spontaneous scalarization of charged black holes (BHs) which is induced by the coupling of the scalar field to the electromagnetic field strength and the double-dual Riemann tensor $L^{mu ualphabeta}F_{mu u}F_{alphabeta}$ in a scalar-vector-tensor theory. In our model, the scalarization can be realized under the curved background with a non-trivial electromagnetic field, such as Reissner-Nordstr$ddot{rm o}$m Black Holes (RN BHs). Firstly, we investigate the stability of the constant scalar field around RN BHs in the model, and show that the scalar field can suffer a tachyonic instability. Secondly, the bound state solution of the test scalar field around a RN BH and its stability are discussed. Finally, we construct scalarized BH solutions, and investigate their stability.
We study static and spherically symmetric charged stars with a nontrivial profile of the scalar field $phi$ in Einstein-Maxwell-scalar theories. The scalar field is coupled to a $U(1)$ gauge field $A_{mu}$ with the form $-alpha(phi)F_{mu u}F^{mu u}/4$, where $F_{mu u}=partial_{mu}A_{ u}-partial_{ u} A_{mu}$ 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 $({rm d}alpha/{rm d}phi) (0)=0$ and $({rm d}^2alpha/{rm d}phi^2) (0)>0$. For the coupling $alpha (phi)=exp (-beta phi^2/M_{rm pl}^2)$, where $beta~(<0)$ is a coupling constant and $M_{rm pl}$ is a reduced Planck mass, there is a branch of charged star solutions with a nontrivial profile of $phi$ 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 $rho_c/rho_m$ between charge density $rho_c$ and matter density $rho_m$ 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 $beta$ 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.
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 evolves into a hairy BH solution. Our analysis will extend the previous studies about the Einstein-scalar-Gauss-Bonnet (GB) theory to other classes of the Horndeski theory. First, we clarify the conditions for the existence of the vanishing scalar field solution $phi=0$ on top of the Schwarzschild spacetime, and we apply them to each individual generalized galileon coupling. For each coupling, we choose the coupling function with minimal power of $phi$ and $X:=-(1/2)g^{mu u}partial_muphipartial_ uphi$ that satisfies the above condition, which leaves nonzero and finite imprints in the radial perturbation of the scalar field. Second, we investigate the radial perturbation of the scalar field about the $phi=0$ solution on top of the Schwarzschild spacetime. While each individual generalized galileon coupling except for a generalized quartic coupling does not satisfy the hyperbolicity condition or realize a tachyonic instability of the Schwarzschild spacetime by itself, a generalized quartic coupling can realize it in the intermediate length scales outside the event horizon. Finally, we investigate a model with generalized quartic and quintic galileon couplings, which includes the Einstein-scalar-GB theory as the special case.
We study the fully nonlinear dynamics of black hole spontaneous scalarizations in Einstein-Maxwell scalar theory with coupling function $f(phi)=e^{-bphi^{2}}$, which can transform usual Reissner-Nordstrom 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 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 a 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 non-linear dynamical study.
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 non-minimal 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 exist. For case (a) we observe that the intervals of existence are mutually exclusive for different $k$.
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