Kerr black holes might have a traversable wormhole without resorting to exotic matter. It could be that particles entering a Kerr black hole end up in another dimension.
What is usually ignored in these speculations is entropy. When we fall into a black hole or a wormhole, we gain entropy. Symmetrically, when we travel out of a wormhole, we would have to lose in entropy.
Someone made a nice analogy for this. If spacetime is a river, a black hole is a waterfall, then the wormhole is a waterfall followed with an inverted waterfall flowing upwards. There is nothing that forbids water to flow to the sky, except the second law of thermodynamics.
So - maybe some matter (in the sense of mass) can enter another dimension via a Kerr black hole, but most probably all information it carries will be destroyed. Rather poor way of travelling, IMO.