In this source explaining how to derive the Schwarzchild metric, the person came up with an ansatz and worked from there. Source: http://www.thescienceforum.com/physics/30059-solving-einstein-field-equations.html [Broken] I just want to know this: How do you come up with a proper ansatz? It looks like the guy in the source just chose any space-time interval of his desire (the one for spherical coordinates in this case) and then multiplied a few of the terms in the interval by some unknown functions of r. How would he know how many unknown functions of r he needed and which terms to multiply them by? Also, recently, I just went about deriving the Christoffel symbol for 4D cylindrical coordinates. I also derived the metric tensor, the inverse metric tensor and the space-time interval before deriving the Christoffel symbol. How would I know what terms within my cylindrical coordinates space time interval should be multiplied by some unknown functions when I create my ansatz? Also, how many terms should be multiplied by some unknown function? If possible, can someone link me to any sources that teach you how to propose a proper ansatz for the Einstein field equations?