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In the present paper, we construct spontaneously scalarized rotating blackhole solutions in dynamical Chern-Simons (dCS) gravity by following the scalarfield evolution in the decoupling limit. For the range of parameters where theKerr black hole becomes unstable within dCS gravity the scalar field growsexponentially until it reaches an equilibrium configuration that is independentof the initial perturbation. Interestingly, the $\mathbb{Z}_2$ symmetry of thescalar field is broken and a strong maximum around only one of the rotationalaxes can be observed. The black hole scalar charge is calculated for twocoupling functions suggesting that the main observations would remainqualitatively correct even if one considers coupling functions/couplingparameters producing large deviations from the Kerr solution beyond thedecoupling limit approximation.

Spontaneously scalarized black holes in dynamical Chern-Simons gravity: dynamics and equilibrium solutions