Global classical solutions to the spherically symmetric Nordström-Vlasov system

Details Global classical solutions to the spherically symmetric Nordström-Vlasov system Global classical solutions to the spherically symmetric Nordström-Vlasov system

2003-11-07

arxiv.org/abs/gr-qc/0311027v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, LaTeX

Scientific paper

Classical solutions of the spherically symmetric Nordstr\"{o}m-Vlasov system are shown to exist globally in time. The main motivation for investigating the mathematical properties of the Nordstr\"{o}m-Vlasov system is its relation to the Einstein-Vlasov system. The former is not a physically correct model, but it is expected to capture some of the typical features of the latter, which constitutes a physically satisfactory, relativistic model but is mathematically much more complex. We show that classical solutions of the spherically symmetric Nordstr\"{o}m-Vlasov system exist globally in time for compactly supported initial data under the additional condition that there is a lower bound on the modulus of the angular momentum of the initial particle system. We emphasize that this is not a smallness condition and that our result holds for arbitrary large initial data satisfying this hypothesis.

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