On global well-posedness for the Einstein-Maxwell-Euler system in Bondi coordinates

We analyze 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. MATHEMATICS SUBJECT CLASSIFICATION (2010). 35A01, 35A02, 35A09, 35B06, 35Q31, 45K05, 76W05, 83C22.