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Abstract We show under the assumption of small data that solutions to the Einstein-Vlasov system with a pure magnetic field and Bianchi I symmetry isotropise and tend to dust solutions. We also obtain the decay rates for the main variables. This generalises part of the work (LeBlanc 1997 Class. Quantum Grav. 14 2281–301) concerning the future behaviour of orthogonal perfect fluids with a linear equation of state in the presence of a magnetic field to the Vlasov case.
Lee et al. (Thu,) studied this question.
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