Given a set of physical laws, one interesting class of question is aimed at finding out the variety of situations those laws allow. For example, is there only a single kind of rotating black hole, or do the laws of general relativity admit an infinite variety of such objects? Theorems addressing this kind of question are generally known as uniqueness theorems – in their purest form, they state that, given a certain set of physical laws and a certain set of additional conditions, there is no more than one configuration of spacetime and matter that fits the bill.

In general relativity, the most famous such theorems are the black hole uniqueness theorems. They are explored in the spotlight text How many different kinds of black hole are there? A different aspect of the question of uniqueness is addressed in the spotlight text The many ways of building an empty, unchanging universe.