About 50 years ago it was shown that one can formulate Einstein's equations of General Relativity as an initial value problem. One specifies data at one moment in time and then one reconstructs the spacetime from this information. Needless to say, it is very difficult to do this in general. Consequently, it is natural to make additional assumptions before trying to deal with the problem. In cosmology for instance, one standard assumption is that the universe is spatially homogeneous and isotropic. What this means is that at a fixed time, the universe looks the same at different points in space (spatial homogeneity) and it also looks the same in different directions (isotropy). When one has made these stringent assumptions the only freedom left is a scale factor, and Einstein's equations reduce to an ordinary differential equation for the scale factor. It is of some interest to try to relax these conditions. If one first drops the isotropy condition, the mathematical problem one ends up with is a system of ordinary differential equations. If one also relaxes the condition of spatial homogeneity, one is confronted with non-linear wave equations. One can still demand that there be no spatial variation in certain spatial directions, so that one gets non-linear wave equations in 1+1 dimensions, 2+1 dimensions or 3+1 dimensions depending on the symmetry | ![]() |