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

Abstract

We analyze the Einstein-Maxwell equations for an irrotational stiff fluid. Under the spherical symmetry assumption on the space-time, in Bondi co- ordinates, 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.