A Family of Static Nested Spheres
The surfaces appear as round spheres (when we plot loci in polar spherical fashion), and from the form of the line element, we see that the metric restricted to any of these surfaces is
That is, these nested coordinate spheres do in fact represent geometric spheres, but the appearance of rather than shows that the radial coordinate does not correspond to area in the same way as for spheres in ordinary euclidean space. Compare Schwarschild coordinates, where the radial coordinate does have its natural interpretation in terms of the nested spheres.
Read more about this topic: Isotropic Coordinates
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