There's not much to discuss really. Write down the Schwarzschild metric in Kruskal coordinates so that you get both event horizons (the one in region II and the one in region III), take a ##V = \text{const.}##, ##\theta = \frac{\pi}{2}## slice of the Schwarzschild metric in Kruskal coordinates, and embed the resulting 2-manifold into ##\mathbb{R}^{3}##. The resulting embedding diagram will be a dynamic wormhole whose mouth closes before any time-like worldline or null geodesic can pass through it using classical energy methods.