Global Static Solutions of the Spherically Symmetric Vlasov-Einstein-Maxwell (VEM) System for Low Charge

DOI: 10.4236/apm.2013.31016   PDF   HTML   XML   4,388 Downloads   6,116 Views   Citations

Abstract

We consider the VEM system in the context of spherical symmetry and we try to establish a global static solutions with isotropic pressure that approaches Minkowski spacetime at infinity and have a regular center. To be in accordance with numerical investigation we take here low charge particles.

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P. Noundjeu, "Global Static Solutions of the Spherically Symmetric Vlasov-Einstein-Maxwell (VEM) System for Low Charge," Advances in Pure Mathematics, Vol. 3 No. 1, 2013, pp. 121-126. doi: 10.4236/apm.2013.31016.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] G. Rein and A. D. Rendall, “Smooth Static Solutions of the Spherically Symmetric Vlasov-Einstein System,” Annales de l’Institut Henri Poincaré, Vol. 59, No. 4, 1993, pp. 383-397.
[2] J. Batt, “Global Symmetric Solutions of the Initial Value Problem in Stellar Dynamics,” Journal of Differential Equations, Vol. 25, No. 3, 1977, pp. 342-364. doi:10.1016/0022-0396(77)90049-3
[3] P. Noundjeu, “The Einstein-Vlasov-Maxwell System with Spherical Symmetry,” Ph.D. Thesis, Technical University of Berlin, Berlin, 2005.
[4] P. Noundjeu and E. Ngondiep, “On the Non-Relativistic Limit of the Spherically Symmetric Einstein-Vlasov-Max-well System,” Annales de la Faculté des Sciences Université de Yaoundé I, Vol. 37, No. 1, 2010, pp. 1-15.
[5] G. Rein and A. D. Rendall, “The Newtonian Limit of the Spherically Symmetric Vlasov-Einstein System,” Communications in Mathematical Physics, Vol. 150, No. 3, 1992, pp. 585-591. doi:10.1007/BF02096963
[6] J. Smoller, A. Wassermann, S. T. Yau and J. McLeod, “Smooth Static Solutions of the Einstein-Yang-Mills Equations,” Communications in Mathematical Physics, Vol. 143, No. 1, 1991, pp. 115-147. doi:10.1007/BF02100288
[7] A. Schulze, “Existence and Stability of Static Shells for the Vlasov-Poisson System with Fixed Central Point Mass,” math-ph/08031775, 2008.
[8] G. Rein and A. D. Rendall, “Commpact Support of Spherically Symmetric Equilibria in Non-Relativistic and Relativistic Galactic Dynamics,” Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 128, No. 2, 2000, pp. 363-380. doi:10.1017/S0305004199004193
[9] H. Andréasson, M. Eklund and G. Rein, “A Numerical Investigation of the Steady States of the Spherically Symmetric Einstein-Vlasov-Maxwell System,” Classical and Quantum Gravity, Vol. 26, No. 14, 2009, Article ID: 145003. doi:10.1088/0264-9381/26/14/145003
[10] P. Noundjeu, N. Noutchegueme and A. D. Rendall, “Existence of Initial Data Satisfying the Constraints for the Spherically Symmetric Einstein-Vlasov-Maxwell System,” Journal of Mathematical Physics, Vol. 45, No. 2, 2004, pp. 668-676. doi:10.1063/1.1637713

  
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