Interior Schwarzschild problem and its integration

The interior Schwarzschild metric for a static, spherically symmetric perfect fluid can be parametrized with two independent functions of the radial coordinate. These functions are easily expressed in terms of (radial) integrals involving the fluid energy density and pressure. The pressure is, however, not independent, but is determined in terms of the density by one of Einstein's equations, the Oppenheimer-Volkov (OV) equation. An approximate integral to the OV equation is presented which is accurate for slowly varying, realistic, densities, and exact in the constant-density limit. It makes it possible to find completely integrated accurate solutions to the interior Schwarzschild metric in terms of the density only. Some post-Newtonian consequences of the solution are given as well as the resulting general relativistic pressure for an energy density (infinity)r(-1/2).