 In GTR, we specify a model of the universe by giving a triple of three mathematical objects, &lt;M, g,T&gt;. M represents a continuous “manifold”: that means a sort of unstructured space (-time), made up of individual points and having smoothness or continuity, dimensionality (usually, 4-dimensional), and global topology, but no further structure. What is the further structure a space-time needs? Typically, at least, we expect the time-direction to be distinguished from space-directions; and we expect there to be well-defined distances between distinct points; and also a determinate geometry (making certain continuous paths in M be straight lines, etc.). All of this extra structure is coded into g, the metric field. So M and g together represent space-time. T represents the matter and energy content distributed around in space-time (if any, of course).