SpaceTime2D
The metric tensors of two spacetime manifolds, which are arbitrary in nature, are added to provide the metric tensor of a third 'combined' spacetime.
The Ricci tensor calculated for this 'combined' spacetime, which is 2-dimensional and embedded in a flat 3-dimensional spacetime, is shown to be zero.
In the 4-dimensional spacetime of general relativity Einstein's equations reduce to the Ricci tensor being zero where space is empty.
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Download the script: SpaceTime2D.ijs