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On the future of solutions to the massless Einstein–Vlasov system in a Bianchi I cosmology

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Abstract

We show that massless solutions to the Einstein–Vlasov system in a Bianchi I space-time with small anisotropy, i.e. small shear and small trace-free part of the spatial energy momentum tensor, tend to a radiation fluid in an Einstein–de Sitter space-time with the anisotropy \(\Sigma ^a_b\Sigma ^b_a\) and \(\tilde{w}^i_j \tilde{w}^j_i\) decaying as \(O(t^{-\frac{1}{2}})\).

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Acknowledgements

The authors thank Prof John Stalker of Trinity College Dublin for helpful discussions. H.L. and P.T. acknowledge financial support from ICMAT. H.L. was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2018R1A1A1A05078275). EN acknowledges support from grants MTM2017-86875-C3-1-R AEI/ FEDER, UE and RTC-2017-6593-7 AEI/FEDER, UE.

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Authors and Affiliations

  1. Department of Mathematics, Research Institute for Basic Science, Kyung Hee University, Seoul, 02447, Republic of Korea

    Ho Lee

  2. Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), 28049, Madrid, Spain

    Ernesto Nungesser

  3. Department of Mathematics, Universidad Politécnica de Madrid, 28040, Madrid, Spain

    Ernesto Nungesser

  4. Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK

    Paul Tod

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  1. Ho Lee
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  2. Ernesto Nungesser
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  3. Paul Tod
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Correspondence to Ernesto Nungesser.

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Lee, H., Nungesser, E. & Tod, P. On the future of solutions to the massless Einstein–Vlasov system in a Bianchi I cosmology. Gen Relativ Gravit 52, 48 (2020). https://doi.org/10.1007/s10714-020-02699-7

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