New method for extracting static equilibrium configurations in general relativity

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Abstract
We investigate the static equations of general relativity for spherical symmetry in Schwarzschild coordinates. A new formalism is discussed which allows integration of the equations for an isotropic fluid under a broad range of initial assumptions. We are able to derive many previous solutions using this technique, and find as well a number of new solutions to the equations. A process is discussed whereby already known solutions can be generalized to increase their flexibility and usefulness with regard to the mathematical modeling of ultradense objects such as neutron stars.