Split Flows in Bubbled Geometries

We propose a procedure to clarify part of the physical sector in the five dimensional bubble geometries based on ideas similar to the split attractor flow conjecture proposed by Denef. This procedure involves building some simple tree-like graphs that we call skeletons without referring to the moduli space. The skeleton (tree) exists if and only if it passes the existence conditions which are purely based on some local CTC's (closed timelike curves) checking. Then, we propose the conjecture similar to Denef's version which states that every existing skeleton (tree) should correspond to some solution in which the global absence of CTC's is ensured. Furthermore, we propose two pictures to identify this correspondence explicitly and use some numerical examples to show how this procedure works. We also analyze the physical sector of the simplest bubbled supertube and see how the existence conditions constrain the charge parameter space.