The Goursat Problem for the Einstein-Vlasov System: (I) The Initial Data Constraints

Details The Goursat Problem for the Einstein-Vlasov System: (I) The Initial Data Constraints The Goursat Problem for the Einstein-Vlasov System: (I) The Initial Data Constraints

2011-09-30

arxiv.org/abs/1109.6844v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, No figures

Scientific paper

We show how to assign, on two intersecting null hypersurfaces, initial data for the Einstein-Vlasov system in harmonic coordinates. As all the components of the metric appear in each component of the stress-energy tensor, the hierarchical method of Rendall can not apply strictly speaking. To overcome this difficulty, an additional assumption have been imposed to the metric on the initial hypersurfaces. Consequently, the distribution function is constrained to satisfy some integral equations on the initial hypersurfaces.

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