  We consider a spherically symmetric characteristic initial value problem for
the Einstein-Maxwell-scalar field equations. On the initial outgoing
characteristic, the data is assumed to satisfy the Price law decay widely
believed to hold on an event horizon arising from the collapse of an
asymptotically flat Cauchy surface. We establish that the heuristic mass
inflation scenario put forth by Israel and Poisson is mathematically correct in
the context of this initial value problem. In particular, the maximal domain of
development has a future boundary, over which the spacetime is extendible as a
continuous metric, but along which the Hawking mass blows up identically; thus,
the spacetime is inextendible as a differentiable metric. In view of recent
results of the author in collaboration with I. Rodnianski (gr-qc/0309115),
which rigorously establish the validity of Price's law as an upper bound for
the decay of scalar field hair, the continuous extendibility result applies to
the collapse of complete asymptotically flat spacelike data where the scalar
field is compactly supported on the initial hypersurface. This shows that under
Christodoulou's C^0 formulation, the strong cosmic censorship conjecture is
false for this system.
