No-hair conjecture for Einstein-Plebanski nonlinear electrodynamics static black holes

The no-hair conjecture statement is enhanced to include static regular and singular black-hole solutions, based on the class of nonlinear electrodynamics proposed by Plebanski coupled to Einstein theory. In particular, we focus, as example, on regular black-hole solutions, i.e., black holes where the space-time metric everywhere is nonsingular, in the framework of General Relativity theory. Time-reversal invariance implies the existence of two separate non-overlapping cases: a purely gravito-electric case, and a purely gravito-magnetic one. We prove the enhanced no-hair conjecture for both cases. Moreover, the generalization of the conjecture including also the couplings to non-Abelian matter is also discussed.