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uniqueness

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.

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uniqueness

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.

uniqueness theorems (uniqueness)

spacetime

Already in special relativity, observers in motion relative to each other will not, in general, agree as to whether two events happen simultaneously, or as to how great is the distance between two objects. They do, however, agree as to what events there are, although not to when and where they happen. This observer-independent totality of all events is called spacetime. How spacetime is split into space and time can differ from observer to observer. Every-day space has three dimensions. Adding time adds another dimension - spacetime has four dimensions, all in all. We are used to the idea of a point in space - an object that has only one location and is completely defined once its space coordinates are given. In spacetime, a spacetime point is an object defined completely once its space coordinates and its time coordinate are given - which makes a spacetime point nothing but an elementary event. The idea of spacetime is, in addition to its role in special relativity, a building block of general relativity. Analogous to how a plane is flat, but the surface of a sphere is curved, in general relativity, curved or distorted versions of the simple, flat spacetime of special relativity play a role. Spacetime curvature, in general relativity, is intimately connected with gravity. For an introduction to the basics of both theories of relativity, check out the chapters Special relativity and General relativity in Elementary Einstein. Sometimes, it can be helpful to view spacetime in analogy to ordinary space - such analogies are explored in the spotlight topics Time dilation on the road (for time dilation) and Twins on the road (for the twin effect).

matter

In general relativity: All contents of spacetime that contribute to its curvature: particles, dust, gases, fluids, electromagnetic and other fields. In particle physics: All elementary particles with half-integer spin, such as electrons and quarks, as well as their composites such as protons and neutrons, in contrast with force particles.

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uniqueness

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