Embedding Gauss–Bonnet Scalarization Models in Higher Dimensional Topological Theories

In the presence of appropriate non-minimal couplings between a scalar field and curvature squared Gauss–Bonnet (GB) term, compact objects such as neutron stars black holes (BHs) can spontaneously scalarize, becoming preferred vacuum. Such strong gravity phase transitions have attracted considerable attention recently. The coupling functions that allow this mechanism are, however, always postulated ad hoc. Here, we point out families naturally emerge in context Higgs–Chern–Simons models, which are found dimensionally descents higher dimensional, purely topological, Chern–Pontryagin non-Abelian densities. As proof concept, study spherically symmetric scalarized BH solutions particular Einstein-GB-scalar model, whose is obtained from construction, pointing novel features caveats thereof. possibility vectorization also discussed, since construction originates vector fields non-minimally coupled to GB invariant.