"In 2+1 dimensions, Einstein's equation in a vacuum requires that spacetime is completely flat. This is in stark contrast to the situation in 3+1 dimensions, where the vacuum solutions are only required to be “Ricci flat”, that is, the Ricci curvature tensor must be zero, but the complete, Riemann curvature tensor need not be, allowing for gravitational waves, and for the familiar gravitational effects of the sun on the Earth, and so on."
5 out of 5
http://www.gregegan.net/SCIENCE/GR2plus1/GR2plus1.html
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