Compute the equations

The equations are second-order nonlinear partial DE's in general but things often simply when there are symmetries. In our case we have rotational symmetry (a point mass looks the same from all directions in space) and time-translation symmetry (the point mass isn't jumping around or doing anything, it will look exactly the same ten minutes from now as it did 10 million years ago, etc.) PLUS the equations have to be independent of transformations in coordinates.

How many equations will we really have to solve?

The curvature side of the equations

The stress-energy side of the equations

Look at the full set of equations

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What is the spacetime geometry?