Algorithmic construction of static perfect fluid spheres

Perfect fluid spheres, either Newtonian or relativistic, are the first step in developing realistic stellar models (or models for fluid planets). Despite the importance of these models, explicit and fully general solutions of the perfect fluid constraint in general relativity have only very recently been developed. In this paper we present a variant of Lake's algorithm wherein (1) we recast the algorithm in terms of variables with a clear physical meaning---the average density and the locally measured acceleration due to gravity, (2) we present explicit and fully general formulas for the mass profile and pressure profile, and (3) we present an explicit closed-form expression for the central pressure. Furthermore we can then use the formalism to easily understand the pattern of interrelationships among many of the previously known exact solutions, and generate several new exact solutions.