Construction and physical properties of Kerr black holes with scalar hair

Kerr black holes with scalar hair are solutions of the Einstein-Klein-Gordon field equations describing regular (on and outside an event horizon), asymptotically flat black holes with scalar hair (arXiv:1403.2757). These black holes interpolate continuously between the Kerr solution and rotating boson stars in D=4 spacetime dimensions. Here we provide details on their construction, discussing properties of the ansatz, the field equations, the boundary conditions and the numerical strategy. Then, we present an overview of the parameter space of the solutions, and describe in detail the space-time structure of the black holes exterior geometry and of the scalar field for a sample of reference solutions. Phenomenological properties of potential astrophysical interest are also discussed, and the stability properties and possible generalizations are commented on. As supplementary material to this paper we make available numerical data files for the sample of reference solutions discussed, for public use.