metric

A measure of distance in space or spacetime that is the same for all observers regardless of their state of motion. In ordinary Euclidean geometry, distances (s) are expressed in terms of the coordinates x, y and z, by s2 = x2 + y2 + z2. This is the metric in three-dimensional Euclidean space. For astronomy and cosmology, the term metric has special importance when the geometrical properties of the universe at large are considered. By introducing time as the fourth dimension, Einstein set out the concept of an "interval" in the spacetime continuum, given by the metric s2 = t2 - (x2 + y2 + z2)/c2. The inclusion of time in this metric ensures that measurements of intervals do not change (are invariant) in frames of reference that are in relative motion. Matter in the universe causes spacetime to be curved. Various ways of describing different sorts of curvature mathematically lead to different metrics. The simple metric given above is the Minkowski metric, which would apply in an infinite universe containing no matter. The metrics used in more realistic models, such as the Robertson-Walker metric or Kerr metric, are more complex.