Spontaneously Scalarized Kerr Black Holes in Extended Scalar-Tensor-Gauss-Bonnet Gravity.

We construct asymptotically flat, spinning, regular on and outside an event horizon, scalarized black holes (SBHs) in extended scalar-tensor-Gauss-Bonnet models. They reduce to Kerr BHs when the scalar field vanishes. For an illustrative choice of nonminimal coupling, we scan the domain of existence. For each value of spin, SBHs exist in an interval between two critical masses, with the lowest one vanishing in the static limit. Non-uniqueness with Kerr BHs of equal global charges is observed; the SBHs are entropically favoured. This suggests that SBHs form dynamically from the spontaneous scalarization of Kerr BHs, which are prone to a scalar-triggered tachyonic instability, below the largest critical mass. Phenomenologically, the introduction of BH spin damps the maximal observable difference between comparable scalarized and vacuum BHs. In the static limit, (perturbatively stable) SBHs can store over 20% of the spacetime energy outside the event horizon; in comparison with Schwarzschild BHs, their geodesic frequency at the ISCO can differ by a factor of 2.5 and deviations in the shadow areal radius may top 40%. As the BH spin grows, low mass SBHs are excluded, and the maximal relative differences decrease, becoming of the order of a few percent for dimensionless spin j≳0.5. This reveals a spin selection effect: non-GR effects are only significant for low spin. We discuss if and how the recently measured shadow size of the M87 supermassive BH constrains the length scale of the Gauss-Bonnet coupling.