Spontaneous scalarization is a mechanism that endows relativistic stars and black holes with a nontrivial configuration only when their spacetime curvature exceeds some threshold. Beyond this threshold, they acquire a nontrivial scalar configuration, which also affects their structure. The onset of scalarization is controlled only by terms that contribute to linear perturbation around solutions of general relativity. I will present the complete set of these terms in generalized scalar-tensor theories, and determine the relevant thresholds in terms of the contributing coupling constants and the properties of the compact object.
Antoine just described spontaneous scalarizations and the state-of-the-art in a webinar on gravity to the SISSA/IFPU group, see it here https://grams-815673.wixsite.com/2019/local-seminars