A rotating black hole, such as a Kerr black hole, has many parts to it. Let us look at the structure of a black hole a little more closely:
1. Event Horizon - The event horizon of a black hole is a boundary in space-time where light and matter can only enter the black hole. Matter and light falling inwards pass the event horizon and can only move towards the center of the black hole. Nothing escapes the event horizon once it is within. The name itself refers to an event occurring within the horizon from which information of the event cannot reach an observer outside, hence the event can never be known. So what really happens as one approaches the event horizon of a black hole (assuming the gravity of the black hole does not break down the matter into individual atoms)? To an observer watching someone nearing the event horizon, time begins to slow down. This is due to gravitational time dilation and as one nears the event horizon, it appears to take infinitely long to reach it. Processes begin to slow down. As a result the light emitted from the person approaching the black hole appears redder and dimmer due to gravitational redshifting. After an infinitely long time, the observer sees the person approaching very close to the event horizon and the light becomes so dim that the person can no longer be seen. To the person entering the black hole, all events happen normally and they enter the event horizon in a finite time
2. Ergosphere - The ergosphere is an ellipsoidal region located just outside the black hole, such as the poles which touch the event horizon. The ergosphere is a region in which an effect known as frame-dragging occurs, making it impossible for someone to stand still within. In this process, space-time is dragged in the direction of the rotating black hole at speeds greater than the speed of light in the observable universe. As a consequence, one cannot maintain a fixed position unless they travel faster than the speed of light. Since the ergosphere is situated outside the event horizon, one can still theoretically escape. If a spaceship enters the ergosphere and then escapes, it will take part of the energy of the black hole with it and the rotating black hole will lose its spin and the ergosphere will cease to exist. This process is known as the Penrose process and powerful gamma ray bursts observed in the universe are thought to be a result of this.
3. Accretion Disk - An accretion disk forms around the black hole consisting of matter that forms an omni-directional cloud around the black hole. Matter in the disk gradually falls into the black hole and the accretion disk is visible as long as the black hole has a continual source of matter.
4. Photon Sphere - A photon sphere is a region where photons are forced to travel in orbits around the black hole due to the gravitational influence of the black hole. The orbits are not very stable so any minor disturbance can cause the photons to either escape from the sphere or cause an inward spiral passing the event horizon and eventually reaching the center of the black hole.
5. Singularity - The singularity is the center of the black hole where space-time becomes infinitely curved. The singularity is infinitely dense and the laws of physics break down here as matter reaches its presence. Keep in mind, however, that the singularity has no volume. For non-rotating black holes the singularity takes the shape of a single point, whereas for rotating black holes, it forms a ring singularity. Assuming one can survive the tidal forces within the black hole, once you reach the singularity you will be crushed to infinite density and all the mass of your body will be added to the volume of the black hole. Within a rotating black hole, it is possible to avoid the singularity and theoretically exit the black hole into a different region of space many millions of light years away or even in a different universe through a wormhole. Another theoretical possibility within rotating black holes is following closed time-like curves around the singularity. This would mean one can travel to the past or into the future.