Embedding Negatively Curved Initial Data on Black-Hole Collisions in R

Visualizing the evolution of gravitating systems can be of considerable conceptual value, because it provides important physical information about those systems such as initial data for the problem of the head-on collision of two black holes. This paper discusses several systems for isometrical embedding in R3, which is equivalent to visualization. We provide some basic analysis on isometric embedding in R3 and historical remarks. The Schwarzschild initial surface is the only one that can be visualized with any degree of completeness. We show explicit reasons for the uniqueness of the visualization of the Schwarzschild initial surface. keyword: negatively curved surfaces, isometrical embedding, collisions of black holes.