  We construct examples of codimension two hyperbolic link complements in
closed smooth 4-manifolds with homeomorphism type $\#_{2k}S^2 \times S^2$. All
our examples are based on a construction of J. Ratcliffe and S. Tschantz, who
constructed 1171 non-compact finite volume hyperbolic 4-manifolds of minimal
volume. We then give necessary conditions for a closed smooth simply connected
4-manifold to contain a codimension two link complement that admits a
hyperbolic structure.
