A fluid sphere in general relativity

We solve the Einstein field equations for the interior of a static fluid sphere in closed analytic form. The model sphere obtained has a physically reasonable equation of state, and a maximum mass of 2/5 the fluid radius (in geometric units). As the maximum mass is approached the central density and pressure become infinite, while for masses greater than about 0.35 times the fluid radius the velocity of sound in portions of the fluid exceeds the velocity of light, indicating that the fluid is noncausal in this mass range. In the low mass limit the solution becomes identical to the Schwarzschild interior solution.