Image:Pith helmet.gif

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[edit] Summary

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.

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.

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

$z(r) = 10-\sqrt{125-r^2}, \; 0 < r < 5$

$z(r) = -4 + 2 \sqrt{r-1}, \; 5 < r < \infty$

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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	Date/Time	Dimensions	User	Comment
current	16:24, 18 October 2005	400×400 (2 KB)	Hillman (Talk \| contribs)	(This is an illustration of a three-dimensional hyperslice of a simple example of static spherically symmetric perfect fluid solution, with one dimension supressed, embedded in a flat euclidean spacetime for ease of visualizing the geometry. The figure sh)