In Chapter 1, we introduced the concept of a mass singularity,forming in gravitational collapse, and surrounded by an event horizon. Examples of such objects that are not spinning are called Schwarzschild black holes and this term specifically denotes black holes that are not rotating: in the jargon, they have no spin.Simply put, the only characteristic that distinguishes one Schwarzschild black hole from another (other than location) is how massive it is. In Chapter 7 we will learn how black holes grow but for now, it will suffice to know that collapse under gravity is the key ingredient. If there is any rotation whatsoever in the pre-collapsed matter, however gentle, then as the collapse occurs the rotation rate will increase (unless something acts to stop that happening). This arises due to a remarkable physical law known as the conservation of angular momentum. This law is illustrated by a pirouetting skater: as she pulls her arms in she spins faster. In the same way, if the star that gives rise to the black hole is gently rotating then the black hole that it ultimately forms will be spinning significantly and is termed a Kerr black hole. Most stars are in fact rotating, because they themselves are formed from the gravitational collapse of slowly rotating massive gas clouds. (If such a gas cloud had even a minute amount of net rotation then the collapsing cloud will have non-zero angular momentum, and as the matter occupies an increasingly smaller volume the final rotation of the collapsed object may well be rather rapid.) Thus we see that rotation, more commonly called spin, is likely to be a prevalent, if not actually a ubiquitous, characteristic for black holes that have just formed from the collapse of matter.We now believe that spin is as inevitable in real astrophysical black holes as it is in current-day politics (though in the latter case it arises from something other than the conservation of angular momentum!).
We have now stated that a second physical parameter, that of spin or angular momentum, is a characteristic that distinguishes one black hole from another just as mass does. Thus, there are two properties of black holes that are important to keep in mind as we study the behaviour of black holes: mass and spin. In principle,there is a third characteristic of black holes that might be relevant to their behaviour: electrical charge. This is also a conserved quantity in physics, and the forces between electric charges,known as electrostatic forces, have a number of resemblances to gravitational force. A key similarity is that both are (on large scales) examples of inverse-square laws meaning that, in the case of two massive objects, as you double the distance that separates them from one another the gravitational force they experience reduces to a quarter of the original value. A key difference is that while gravity is always attractive, electrostatic charges are only sometimes attractive (when the two bodies are oppositely charged,i.e. one is positive and the other is negative). They are at other times repulsive (when the bodies have charge of the same sign,either both positive or both negative, they repel each other). If two charged bodies have the same type of charge, then electrostatic repulsion will tend to prevent them coalescing, even if gravity is tending to attract them. So while charge could in principle be a third property of black holes that one might hope to measure,in reality a charged black hole would be rapidly neutralized by the surrounding matter. It is therefore a good operational assumption that there are only two relevant properties of black holes that distinguish one from another: mass and spin.That's all!