Department of Mathematics, Faculty of Science, University of Yaounde 1, PO Box 812, Yaounde, Cameroun
PhD student-researcher at the University of Yaoundé I in mathematics (option: Analysis, specialty: Partial Differential Equation).
We study the global asymptotic stability of the Minkowski spacetime for the Einstein-Vlasov-Maxwell system under spherically symmetric perturbations. Here, the Einstein-Vlasov system coupled with the Maxwell equations models
the time evolution of self-gravitating collisionless massive charged particles in the context of general relativity. The particles could be for instance the electrons in a plasma. P. Noundjeu proved that given asymptotically flat initial data which satisfy a smallness condition and when the shift function is equal to zero, which corresponds to the Schwarzschild coordinates, there exist global in time non-trivial solutions to the Einstein-Vlasov-Maxwell system. In this thesis, we extend this result to the case of nonzero shift vector, that allows the metric to be non diagonal one. To do this, we start by writing down our system, using 1+3 formulation. We use ODE techniques to construct initial data that satisfy the constraints. Having the latter in hand, we define via the iterate scheme a sequence of functions that converges to the unique locale solution of our initialboundary value problem. This solution can be extended to the global one, by proving one continuation criterion theorem. We end this work by proving that the obtained spacetime is found to be asymptotically Minkowskian and geodesically complete.