Scalarized 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 $R_{\rm GB}:=R^2-4R^{\alpha\beta}R_{\alpha\beta}+R^{\alpha\beta\mu\nu}R_{\alpha\beta\mu\nu}$ 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.