Weanalyze the Einstein-Maxwell equations for an irrotational stiff fluid.
Under the spherical symmetry assumption on the space-time, in Bondi coordinates,
the considered model is reduced to a nonlinear evolution system of
partial integrodifferential equations. Assuming regularity at the center of
symmetry and that the matter content of the initial light cone is the so-called null
dust, the characteristic initial value problem associated to the obtained system is
solved globally by a contraction mapping argument. In future work we will
address the issue of global well-posedness for the considered model in other
physically interesting cases where the matter content of the initial light cone is
not the null dust.