In a certain class of scalar-Gauss-Bonnet gravity, the black holes and the neutron stars can undergo spontaneous scalarization - a strong gravity phase transition triggered by a tachyonic instability due to the non-minimal coupling between the scalar field and the spacetime curvature. Studies of this phenomenon have so far been restricted mainly to the study of the tachyonic instability and stationary scalarized black holes and neutron stars. Up to date there has been proposed no realistic physical mechanism for the formation of isolated scalarized black holes and neutron stars. We study for the first time the stellar core collapse to a black hole and a neutron star in scalar-Gauss-Bonnet theories allowing for a spontaneous scalarization. We show that the core collapse can produce scalarized black holes and scalarized neutron stars starting with a non-scalarized progenitor star.
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