You raise a valid point. Black holes, by definition, have an event horizon beyond which no information can escape, making direct observations of their internal properties impossible. However, scientists infer the properties of black holes based on their effects on surrounding matter and the behavior of objects in their vicinity.
Angular momentum is a fundamental physical quantity that is conserved in isolated systems, including black holes. When a star collapses to form a black hole, its angular momentum is also conserved. This means that the resulting black hole retains the angular momentum of the original star.
The effects of angular momentum can be observed indirectly in the behavior of matter falling into a black hole. As matter spirals toward the black hole, it forms an accretion disk, a rotating disk of hot gas and dust. The angular momentum of the infalling matter causes the accretion disk to rotate around the black hole. By studying the characteristics of this accretion disk, such as its temperature and the emitted radiation, scientists can infer the angular momentum of the black hole.
Additionally, the study of black hole mergers and their gravitational waves can provide insights into their properties, including angular momentum. When two black holes merge, the resulting black hole carries the combined angular momentum of the original two objects. By detecting and analyzing the gravitational waves emitted during such events, scientists can indirectly measure the angular momentum of the black holes involved.
While direct observation of a black hole's internal structure is impossible, the effects of angular momentum can be deduced through its influence on surrounding matter and the behavior of gravitational waves.