Evaluate curvature at specific points

Question

Let's say I want to create a plot similar to the image below, but with two masses located at e.g. $x_0, y_0, z_0, 0$ and $x_1, y_1, z_1, 0$. How do I compute the curvature $g_{}$ at specific coordinates, e.g. $x, y, z, t = 17, 17, 17, 0$ given a mass e.g. at origo with mass $m$ (or $1$ if that's easier). If this doesn't make sense, consider something that does make sense, e.g. a uniform mass distribution within a radius $r$ around origo. Likewise, if the choice of coordinates ($x, y, z, t$) does not make sense, please feel free to suggest something that does make sense.

Note: A symbolic/exact solution is not necessary. It's enough if there is some equation-system, partial differential equation system or similar that can be solved numerically.

Answer 1

This image can be generated using ordinary Newtonian gravity. There is no need to do anything specifically relativistic here.

To generate this image simply start with a large number of test masses, arranged along the lines of this grid. Connect them to form a regular unbent grid. Then, allow the test masses to all free fall for a time. Connect them to form the bent grid in the picture.