Rotating Black Holes

Abstract The Chapter is devoted to rotating black holes, their properties, global structure, and study particle and light motion in their gravitational field. We introduce and explain notions of the horizon and ergosurface in the Kerr geometry, study the extreme rotating limit of the Kerr black hole. We discuss how the rotation of the black hole affects main characteristics of the particle trajectories, in particular the radius of the innermost stable orbit and the energy of a particle at this orbit. We describe a twin paradox for inertial observers moving along circular orbits induced by the black hole rotation. We describe hidden symmetries that are responsible for the complete integrability of the geodesic equations in the Kerr spacetime. As a result of accretion of matter from the accretion disk the velocity of rotation of the black holeincreases. We discuss this effect in detail. Observable properties of the Kerr black hole, including the shadow effect, are considered. Energy extraction processes, in particular the Penrose process and superradiance, are studied. We discuss also weakly magnetized rotating black hole and a possible role of the magnetic field in the energy extraction.