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
Famous quotes containing the words family, nested and/or spheres:
“It was occasions like this that made me more resolved than ever that my family would someday know real security. I never for a moment doubted that I myself would ultimately provide it for them.”
—Mary Pickford (1893–1979)
“A million people—manners free and superb—open
voices—hospitality—the most courageous and friendly young men,
City of hurried and sparkling waters! city of spires and masts!
City nested in bays! my city!”
—Walt Whitman (1819–1892)
“Perhaps a modern society can remain stable only by eliminating adolescence, by giving its young, from the age of ten, the skills, responsibilities, and rewards of grownups, and opportunities for action in all spheres of life. Adolescence should be a time of useful action, while book learning and scholarship should be a preoccupation of adults.”
—Eric Hoffer (1902–1983)