Rendiconti del Seminario Matematico della Università di Padova
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Published online: 2014-06-08
On global well-posedness for the Einstein-Maxwell-Euler system in Bondi coordinatesMamadou Sango and Calvin Tadmon (1) University of Pretoria, South Africa
(2) University of Dschang, Cameroon
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.
Keywords: Characteristic Cauchy problem, Einstein-Maxwell-Euler equations, spherical symmetry, irrotational perfect fluid, Bondi coordinates
Sango Mamadou, Tadmon Calvin: On global well-posedness for the Einstein-Maxwell-Euler system in Bondi coordinates. Rend. Sem. Mat. Univ. Padova 131 (2014), 179-192. doi: 10.4171/RSMUP/131-10