M.Freedman and R.Gompf's work show that there are at least 13 exotic structures in $S^3\times \mathbb{R}$, which is a open 4-manifold, so now I wonder whether there is an exotic structure in $S^3\times [0,\infty)$ such that its boundary $S^3\times \{0\}$ is a smooth 3-manifold?