- a = 0: This corresponds to a non-rotating black hole, also known as a Schwarzschild black hole. In this case, the black hole's rotation axis is stationary.
- 0 < a < 1: This indicates a rotating black hole. As 'a' increases, the black hole spins faster.
- a = 1: This represents a maximally rotating black hole, also called an extreme Kerr black hole. In this case, the black hole is spinning at the fastest possible rate allowed by the laws of physics. Extreme Kerr black holes are thought to be the most efficient sources of energy extraction through rotational energy.
In reality, most observed black holes are likely rotating at various rates between 0 and 1. The spin rate depends on various factors, including the black hole's formation history and any interactions it may have had with surrounding matter.
For instance, black holes formed from collapsed massive stars are expected to have higher spins because of the star's angular momentum. On the other hand, black holes formed through the mergers of smaller black holes may have lower spins due to the chaotic nature of the merger process.
Observational studies of black holes, particularly through X-ray and radio observations, have provided insights into their spin rates. Some black holes, such as the supermassive black hole at the center of our Milky Way galaxy (Sagittarius A*), are known to be slowly rotating with 'a' values close to 0. On the other hand, other black holes have been observed to be spinning rapidly, approaching 'a' values closer to 1.
