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Register a new userScalarized black holes in the presence of the coupling to Gauss-Bonnet gravity
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In this paper, we study static and spherically symmetric black hole (BH) solutions in the scalar-tensor theories with the coupling of the scalar field to the Gauss-Bonnet (GB) term $xi (phi) R_{rm GB}$, where $R_{rm GB}:=R^2-4R^{alphabeta}R_{alphabeta}+R^{alphabetamu u}R_{alphabetamu u}$ is the GB invariant and $xi(phi)$ is a function of the scalar field $phi$. Recently, it was shown that in these theories scalarized static and spherically symmetric BH solutions which are different from the Schwarzschild solution and possess the nontrivial profiles of the scalar field can be realized for certain choices of the coupling functions and parameters. These scalarized BH solutions are classified in terms of the number of nodes of the scalar field. It was then pointed out that in the case of the pure quadratic order coupling to the GB term, $xi(phi)=eta phi^2/8$, scalarized BH solutions with any number of nodes are unstable against the radial perturbation. In order to see how a higher order power of $phi$ in the coupling function $xi(phi)$ affects the properties of the scalarized BHs and their stability, we investigate scalarized BH solutions in the presence of the quartic order term in the GB coupling function, $xi(phi)=eta phi^2 (1+alpha phi^2)/8$. We clarify that the existence of the higher order term in the coupling function can realize scalarized BHs with zero nodes of the scalar field which are stable against the radial perturbation.
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We report on a numerical investigation of the stability of scalarized black holes in Einstein dilaton Gauss-Bonnet (EdGB) gravity in the full dynamical theory, though restricted to spherical symmetry. We find evidence that for sufficiently small curvature-couplings the resulting scalarized black hole solutions are nonlinearly stable. For such small couplings, we show that an elliptic region forms inside these EdGB black hole spacetimes (prior to any curvature singularity), and give evidence that this region remains censored from asymptotic view. However, for coupling values superextremal relative to a given black hole mass, an elliptic region forms exterior to the horizon, implying the exterior Cauchy problem is ill-posed in this regime.
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We study the instability of the charged Gauss-Bonnet de Sitter black holes under gravito-electromagnetic perturbations. We adopt two criteria to search for an instability of the scalar type perturbations, including the local instability criterion based on the $AdS_2$ Breitenl{o}hner-Freedman (BF) bound at extremality and the dynamical instability via quasinormal modes by full numerical analysis. We uncover the gravitational instability in five spacetime dimensions and above, and construct the complete parameter space in terms of the ratio of event and cosmological horizons and the Gauss-Bonnet coupling. We show that the BF bound violation is a sufficient but not necessary condition for the presence of dynamical instability. While the physical origin of the instability without the Gauss-Bonnet term has been argued to be from the $AdS_2$ BF bound violation, our analysis suggests that the BF bound violation can not account for all physical origin of the instability for the charged Gauss-Bonnet black holes.
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