Internal and external metrics for a perfect fluid cylinder in general relativity

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Abstract
A solution to Einstein’s equations describing a perfect fluid cylinder of finite radius is presented. The proper density μ and pressure p of the fluid are physically well behaved in the radial coordinate range 0≤r≤r1. On the axis (r=0) the solution is regular and μ and p are finite and positive. As r increases μ and p decrease steadily through positive values, p vanishing at r=r1. The ratio p/μ (a (p= (3)/(7) μ−Nμ3/10, where N is a positive constant. The matching metric for the vacuum exterior to the cylinder is given, so that the space‐time is complete and nonsingular.

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