Scalarized black holes in scalar Gauss-Bonnet models with a positive cosmological constant

Since the start of modern Astrophysics and Cosmology, two mysteries have been puzzling researchers: dark energy and dark matter. In order to tackle this, researchers have been trying to get clearer answers through the study alternative gravity models, considering higher curvature terms and/or bosonic scalar fields. The theories of modified gravity that include extra scalar fields, so-called scalar-tensor theories, present some interesting phenomenology. An intriguing possibility occurs when the additional scalar field is non-minimally coupled to the gravitational sector. The interaction between a scalar field and the strong spacetime curvature of a black hole originates what is known as scalarization. The latter endows BHs surrounded by a real scalar field with interesting and distinct characteristics. Alternatively, low-compactness objects that do not have enough curvature can be helped by the presence of a positive cosmological constant, allowing objects like galaxies and galaxy clusters to suffer scalarization, adding an extra mass profile outside of the observable matter. It then follows the possibility for this matter profile to mimic the observed dark matter. For this study, we will consider scalarized objects in an extended scalar-tensor theory where the scalar field is non-minimal coupled through a quartic coupling function to the Gauss-Bonnet invariant and in the presence of a positive cosmological constant. Firstly, the equations of motion for the metric and the scalar field were obtained from the action. Then, through the numerical method Runge-Kutta with a shooting method, the profiles of the scalar field between the Schwarzschild horizon and the cosmological horizon were derived for various values of the coupling constant β and Λ. Finally, plots of β related to the main parameters of the problem have been extracted from the results of the integration and the plots of BH evolutionary branches.