Nonlinear Stability of the Milne Model with Matter

Abstract

AbstractWe show that any $$3+1$$ 3 + 1 -dimensional Milne model is future nonlinearly, asymptotically stable in the set of solutions to the Einstein–Vlasov system. For the analysis of the Einstein equations we use the constant-mean-curvature-spatial-harmonic gauge. For the distribution function the proof makes use of geometric $$L^2$$ L 2 -estimates based on the Sasaki-metric. The resulting estimates on the energy-momentum tensor are then upgraded by employing the natural continuity equation for the energy density. The combination of $$L^2$$ L 2 -estimates and the continuity equation reveals a powerful tool to analyze massive transport equations with potential applications beyond the result presented here.