  This paper is the first part of a trilogy dedicated to the following problem:
given spherically symmetric characteristic initial data for the
Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$,
with the data on the outgoing initial null hypersurface given by a subextremal
Reissner-Nordstrom black hole event horizon, study the future extendibility of
the corresponding maximal globally hyperbolic development (MGHD) as a "suitably
regular" Lorentzian manifold.
  In this first part we establish well posedness of the Einstein equations for
characteristic data satisfying the minimal regularity conditions leading to
classical solutions. We also identify the appropriate notion of maximal
solution, from which the construction of the corresponding MGHD follows, and
determine breakdown criteria. This is the unavoidable starting point of the
analysis; our main results will depend on the detailed understanding of these
fundamentals.
  In the second part of this series we study the stability of the radius
function at the Cauchy horizon. In the third and final paper we show that,
depending on the decay rate of the initial data, mass inflation may or may not
occur; in fact, it is even possible to have (non-isometric) extensions of the
spacetime across the Cauchy horizon as classical solutions of the Einstein
equations.
