  This talk describes some recent results [16] regarding the problem of
uniqueness in the large (also known as strong cosmic censorship) for the
initial value problem in general relativity. In order to isolate the essential
analytic features of the problem from the complicated setting of gravitational
collapse in which it arises, some familiarity with conformal properties of
certain celebrated special solutions of the theory of relativity will have to
be developed. This talk is an attempt to present precisely these features to an
audience of non-specialists, in a way which will hopefully fully motivate a
certain characteristic initial value problem for the spherically-symmetric
Einstein-Maxwell-Scalar Field system. The considerations outlined here leading
to this particular initial value problem are well known in the physics
relativity community, where the problem of uniqueness has been studied
heuristically [1, 22] and numerically [2, 3]. In [16], the global behavior of
solutions to this IVP, in particular, the issue of uniqueness, is
mathematically completely understood. A statement of the relevant Theorems is
included in Section 9. Only a sketch of the ideas of the proof is provided
here, but the readers may refer to [16] for details.
