Kerr black holes with synchronized axionic hair

We construct and analyze Kerr black holes (BHs) with synchronized axionic hair. These are the BH generalizations of the recently constructed rotating axion boson stars [J. F. Delgado, C. A. Herdeiro, and E. Radu, Rotating axion boson stars, J. Cosmol. Astropart. Phys. 06 (2020) 037]. Such BHs are stationary, axially symmetric, asymptotically flat solutions of the complex Einstein-Klein-Gordon theory with a QCD axionlike potential. They are regular everywhere on and outside the event horizon. The potential is characterized by two parameters: the mass of the axionlike particle, m(a), and the decay constant, (f) over tilde (a). The limit (f) over tilde (a) -> infinity recovers the original example of Kerr BHs with synchronized scalar hair [C. A. R. Herdeiro and E. Radu, Kerr Black Holes with Scalar Hair, Phys. Rev. Lett. 112, 221101 (2014)]. The effects of the nonlinearities in the potential become important for (f) over tilde (a) less than or similar to 1. We present an overview of the parameter space of the solutions together with a study of their basic geometric and phenomenological properties, for an illustrative value of the coupling that yields a non-negligible impact of the self-interactions.