This problem is related to General Relativity and specifically Black Holes.
The manifold is a 4-dimensional space-time with a Minkowski inner product (i.e. if $||v|| = 0$, $v$ is not necessarily $0$), A null surface is an embedded 3 dimensional surface where the normal vector has length 0 everywhere on the surface (I.e. a light-like closed surface or horizon). The null surface is determined by the geometry of the space time, specifically it is a consequence of the curvature of the manifold.
My question is, given a horizon or null surface shape , is it possible to calculate the metric tensor that describes a space-time where such a null surface will reside in. Given some boundary conditions (like, the metric approaches the minkowski metric at large distances from the null surface)
Specifically, I was wondering if, given a black hole horizon (some funky shape - like a beveled cube) it was possible to calculate the shape of the collapsing mass that would gives such a horizon.