Studying KARMA (Kerr And Relativistic Matter Around)

Introduction/Objective: The main objective of this study is to develop a generalization of the Kerr metric that can be used to model the initial or intermediate stage of the formation of a rotating black hole. The end result of this process may involve either the complete absorption of matter by the black hole or the formation of a quasi-stable black-hole configuration with an accretion disk consisting of external matter. Methods: Solving the aforementioned tasks involves the use of well-established methods in theoretical physics, based on finding solutions to systems of differential equations, analyzing symmetries, and applying various criteria to describe the dynamics of test particles in the vicinity of massive astrophysical objects. Results: As a result of our research, we derived a series of solutions for a rotating Kerr-type black hole with non-trivial matter on a flat and (A)dS background. Symmetry arguments and singularity analysis in the proposed black hole models allowed us to fix the free parameters of the solutions, while the study of popular energy conditions enabled us to impose constraints on the configuration and field content of the external matter. The resulting spacetime geometry exhibits a singularity of a special type in the directions of the north and south poles, which may be responsible for a bipolar outflow of particles from the black holes. As a step toward constructing a solution for a nonstationary rotating black hole in the presence of matter, we investigated the zero angular momentum limit of the constructed metrics. The use of the Eddington–Finkelstein coordinates allowed us to generalize the proposed construction to a Vaidya-type black hole. Finally, using the Newman–Janis algorithm, we found the corresponding generalization of the solution for the Kerr–Vaidya black hole. Discussion: It is important to note that the general nature of our analysis does not require a specific definition of the fields of matter; it is sufficient that they be described by the standard energymomentum tensor of relativistic matter. A key point in the construction is the connection between the generalization of spacetime geometry proposed here and the original Kerr solution, which implies keeping the fundamental characteristics of the Kerr metric. Conclusion: Our findings represent necessary and important steps toward solving the problem of the formation and evolution of Kerr black holes. Given their importance in astrophysics, these results open new perspectives on the study of compact rotating astrophysical objects, provide new insights into the possible composition of accretion disks, and suggest new ways to explain the mechanisms of formation of ultra-high-energy particle jets from rotating black holes. PACS: 04.70.-s, 04.70.Bw, 04.20.Jb.