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Note that the geometry almost decomposes into a Cartesian product of the y geometry and the x geometry – except that the x-part is warped, i.e. it is rescaled by a scalar function of the other coordinates y. For this reason, the metric of a warped geometry is often called a warped product metric.
Warped geometries acquire their full meaning when we substitute the variable y for t, time and x, for s, space. Then the d(y) factor of the spatial dimension becomes the effect of time that in words of Einstein 'curves space'. How it curves space will define one or other solution to a space-time world. For that reason different models of space-time use warped geometries. Many basic solutions of the Einstein field equations are warped geometries, for example the Schwarzschild solution and the Friedmann–Lemaitre–Robertson–Walker models.