Black hole scalarization from the breakdown of scale invariance

Electrovacuum black holes are scale invariant; their energy-momentum tensor is traceless. Quantum corrections of various sorts, however, can often produce a trace anomaly and a breakdown of scale invariance. The (quantum-corrected) black hole solutions of the corresponding gravitational effective field theory (EFT) have a nonvanishing Ricci scalar. Then, the presence of a scalar field with the standard nonminimal coupling ^2R naturally triggers a spontaneous scalarization of the corresponding black holes. This scalarization phenomenon occurs for an (infinite) discrete set of. We illustrate the occurrence of this phenomenon for two examples of static, spherically symmetric, asymptotically flat black hole solution of EFTs. In one example the trace anomaly comes from the matter sector---a novel, closed form generalization of the Reissner-Nordstr\"om solution with an F^4 correction---whereas in the other example it comes from the geometry sector---a noncommutative geometry generalization of the Schwarzschild black hole. For comparison, we also consider the scalarization of a black hole surrounded by (nonconformally invariant) classical matter (Einstein-Maxwell-dilaton black holes). We find that the scalarized solutions are, generically, entropically favored.