Abstract: We introduce a geometric transition between two homogeneous
three-dimensional geometries: hyperbolic geometry and anti de Sitter
(AdS) geometry. Given a path of three-dimensional hyperbolic
structures that collapse down onto a hyperbolic plane, we describe a
method for constructing a natural continuation of this path into AdS
structures. A particular case of interest is that of hyperbolic cone
structures that collapse as the cone angle approaches $2\pi$. In this
case, the AdS manifolds on the ``other side'' of the transition have
so-called tachyon singularities. We will discuss a general theorem
about this transition and then construct examples using ideal tetrahedra.