**The Cylindrical Symmetry Einstein-Vlasov System with Charged Particles in Expansion
**

* Pierre Noundjeu, David Tegankong *

**Abstract**

We prove the property of being global in time for the solution of the Cauchy problem that corresponds to the cylindrically symmetric Einstein-Vlasov-Maxwell Scalar field (EVMS) system with general (in size) data. It is shown that if there is no singularity at the axis of symmetry, then the local solutions given by Choquet-Bruhat (Ann. Inst. Fourier **21**(3):181–201, 2) can be extended to the global one. We notice that these results generalize those already known for the uncharged case.