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| ==Summary==
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| This is an illustration of a three-dimensional hyperslice of a simple example of static spherically symmetric perfect fluid solution, with one dimension suppressed, embedded in a flat euclidean spacetime for ease of visualizing the geometry.
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| The figure shows a perfect fluid ''interior region'' (gold) matched (with continuous metric and extrinsic curvature tensor) across a spherical surface (represented here as a circle) to a vacuum ''exterior region'' (khaki), which is a portion of the Schwarzschild vacuum solution. | |
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| In this example, the interior region is Schwarzschild's fluid, in which the hyperslices have the geometry of a ''three-spherical cap''. In this example, the embedding is
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| :<math>z(r) = 10-\sqrt{125-r^2}, \; 0 < r < 5 </math>
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| :<math>z(r) = -4 + 2 \sqrt{r-1}, \; 5 < r < \infty</math> | |
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| All static spherically symmetric stellar models resemble the Schwarzschild solution near the center, and are matched to a Schwarzschild vacuum exterior, but other choices of fluid solution for the interior region may differ from the geometry shown here in ways difficult to depict without restoring the suppressed dimension.
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| == Licensing ==
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| {{cc-by-sa-2.5}}
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| {{Copy to Wikimedia Commons|bot=Svenbot|priority=true}}
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Latest revision as of 16:36, 16 December 2014
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