We introduce a systematic and direct procedure to generate hairy rotating black holes by deforming a spherically symmetric seed solution. We develop our analysis in the context of the gravitational decoupling approach, without resorting to the Newman-Janis algorithm. As examples of possible applications, we investigate how the Kerr black hole solution is modified by a surrounding fluid with conserved energy-momentum tensor. We find nontrivial extensions of the Kerr and Kerr-Newman black holes with primary hair. We prove that a rotating and charged black hole can have the same horizon as Kerr’s, Schwarzschild’s, or Reissner-Nordström’s, thus showing possible observational effects of matter around black holes.

• Received 27 September 2020
• Accepted 19 January 2021

DOI:https://doi.org/10.1103/PhysRevD.103.044020