Gravitational decoupling for axially symmetric systems and rotating black holes

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-Nordstrom's, thus showing possible observational effects of matter around black holes.

Automated summary

The study successfully generates rotating black holes with primary hair by deforming spherically symmetric seed solutions, and explores the impact of surrounding fluid on the Kerr black hole solution. The results demonstrate that a rotating and charged black hole may share the same horizon as Kerr's, Schwarzschild's, or Reissner-Nordstrom's, revealing possible observational effects of surrounding matter on black holes.