PHASES OF 4D SCALAR-TENSOR BLACK HOLES WITH NON-LINEAR ELECTRODYNAMICS

According to the no-scalar-hair conjecture, black-hole solutions in scalar-tensor theories of gravity (STT) can be fully classified by their asymptotic preserved charges - mass, electric (magnetic) charge and angular momentum, exactly as in General Relativity (GR). This makes the black holes in STT undistinguishable from those in GR for a distant observer. There is a series of theorems that confirm the conjecture in the vacuum and electrovacuum cases. The present talk is dedicated to new non-unique, numerical solutions that serve as counter-examples of the no-scalar-hair conjecture. They describe charged black holes coupled to non-linear electrodynamics in special classes of STT that posses primary scalar hair.