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Register a new userSpontaneous scalarization of black holes in the Horndeski theory
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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.
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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, 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.
We present an exact static black hole solution of Einstein field equations in the framework of Horndeski Theory by imposing spherical symmetry and choosing the coupling constants in the Lagrangian so that the only singularity in the solution is at $r=0$. The analytical extension is built in two particular domains of the parametric space. In the first domain we obtain a solution exhibiting an event horizon analogous to that of the Schwarzschild geometry. For the second domain, we show that the metric displays an exterior event horizon and a Cauchy horizon which encloses a singularity. For both branches we obtain the corresponding Hawking temperature which, when compared to that of the Schwarzschild black hole, acquires a correction proportional to a combination of the coupling constants. Such a correction also modifies the definition of the entropy of the black hole.
Spontaneous scalarization is a mechanism that endows relativistic stars and black holes with a nontrivial configuration only when their spacetime curvature exceeds some threshold. The standard way to trigger spontaneous scalarization is via a tachyonic instability at the linear level, which is eventually quenched due to the effect of non-linear terms. In this paper, we identify all of the terms in the Horndeski action that contribute to the (effective) mass term in the linearized equations and, hence, can cause or contribute to the tachyonic instability that triggers scalarization.
In the present paper we show the existence of a fully nonlinear dynamical mechanism for the formation of scalarized black holes which is different from the spontaneous scalarization. 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 possessing additional branches with scalar field that turn out to be unstable, though. The formation of scalar hair of the Schwarzschild black hole will always happen with a jump because the stable scalarized branch is not continuously connected to Schwarzschild one.
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