| Summary: | The Einstein-Klein-Gordon Lagrangian is supplemented by a non-minimal coupling of the scalar field to specific geometric invariants: the Gauss-Bonnet term and the Chern-Simons term. The non-minimal coupling is chosen as a general quadratic polynomial in the scalar field and allows – depending on the parameters – for large families of hairy black holes to exist. These solutions are characterized, namely, by the number of nodes of the scalar function. The fundamental family encompasses black holes whose scalar hairs appear spontaneously and solutions presenting shift-symmetric hairs. When supplemented by an appropriate potential, the model possesses both hairy black holes and non-topological solitons: boson stars. These latter exist in the standard Einstein-Klein-Gordon equations; it is shown that the coupling to the Gauss-Bonnet term modifies considerably their domain of classical stability.
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