Waves on static radially symmetric space-times

I will begin by discussing the geometry of the most interesting static radially symmetric space-times: Minkowski space, Schwarzschild black holes, Reissner-Nordstrom black holes, and Reissner-Nordstrom "naked singularities." With the exception of Minkowski space not much is known about long-time behavior of waves on these spaces, but slightly more is known than a few years ago. I will describe some recent progress which is joint work with various subsets of Burq, Klainerman, Machedon, Planchon, and Tahvildar-Zadeh.