The Einstein-Vlasov-Scalar Field System with Gowdy or T2 Symmetry in Contracting Direction

Abstract

We prove in the case of cosmological models for the Einstein-Vlasov-scalar field system with Gowdy symmetry, that the solutions exist globally in the past. The sources of the equations are generated by a distribution function and a scalar field, subject to the Vlasov and the wave equations respectively. The result is generalized for the case of T2 symmetry. Using previous results, we deduce geodesic completeness.

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Acknowledgements

Comments of the anonymous referee are gratefully acknowledged by the authors.

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Correspondence to David Tegankong.

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Tchuani, A.L., Tegankong, D. & Noutchegueme, N. The Einstein-Vlasov-Scalar Field System with Gowdy or T2 Symmetry in Contracting Direction. Acta Math Vietnam 44, 501–517 (2019). https://doi.org/10.1007/s40306-018-0256-1

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Keywords

  • Einstein
  • Vlasov
  • Scalar field
  • Gowdy symmetry
  • T 2 symmetry
  • Hyperbolic differential equations
  • Global existence
  • Geodesic completeness

Mathematics Subject Classification (2010)

  • 83C20
  • 83C22
  • 34B05