Effects like gravitational waves and the curvature surrounding black holes do not occur in spacetimes with one time-like coordinate and two space-like coordinates. This is because the Einstein Field Equations fully constrain the Riemann tensor in fewer than four dimensions.

Are there other interesting effects that exist in four spacial dimensions plus a time-like dimension that vanish in our (3,1) universe? Or is the qualitative difference between (2,1) and (3,1) solely due to the transition between a fully-constrained Riemann tensor and one with freedom?