From some time I have wanted to make an embedding diagram (the partial representation of the space-time curvature under the influence of a gravitational well), and I quote from Wikipedia:

"Consider an idealized rubber sheet suspended in a uniform gravitational field normal to the sheet. In equilibrium, the elastic tension in each part of the sheet must be equal and opposite to the gravitational pull on that part of the sheet; that is,

k (Laplacian operator) h = -g*rho(x)

where k is the elastic constant of the rubber, h(x) is the upward displacement of the sheet (assumed to be small), g is the strength of the gravitational field, and ρ(x) is the mass density of the sheet. The mass density may be viewed as intrinsic to the sheet or as belonging to objects resting on top of the sheet."

But this explanation gives no (direct) hint on the boundary conditions. Now then, would it be valid to consider that h(x) = 0 at the boundaries, and the deformation of the rubber-sheet is given by the function of distribution of ρ(x)? also can we say that ρ(x) is actually ρ(x, y, z), or must it be a vector function, which must be parametrized, so that we would be solving 3 instead of just one PDE? What I want as a final result, is a graphic which would resemble precisely a rubber-sheet (it doesn't have to be a square domain), which has something heavy on the middle.