Spontaneous nonlinear scalarization of Kerr black holes

As it became well known in the past years, Einstein-scalar-Gauss-Bonnet (EsGB) theories evade no-hair theorems and allow for scalarized compact objects including black holes (BH). The coupling function that defines theory is main character process nature of scalarization. With right choice, becomes an extension general relativity (GR) sense any solution to GR field equations remains a EsGB theory, but can destabilize if certain threshold value spacetime curvature exceeded. Thus BHs spontaneously scalarized. most studied driving mechanism this phenomenon tachyonic instability due effective negative squared mass scalar field. However, even when chosen such zero, higher order terms with respect lead what coined nonlinear In paper we investigate how Kerr scalarize by evolving on fixed background via solving Klein-Gordon equation. We consider two different functions terms, one yields non-zero another does not. sweep through parameter space its spin obtain charge end evolution settles equilibrium stationary state. When there no present, probe limit which BH scalarizes zero charge, i.e. gap between bald hairy they only connect goes together charge.