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Lorentz meets Lipschitz

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 نشر من قبل Clemens S\\\"amann
 تاريخ النشر 2020
  مجال البحث فيزياء
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We show that maximal causal curves for a Lipschitz continuous Lorentzian metric admit a $mathcal{C}^{1,1}$-parametrization and that they solve the geodesic equation in the sense of Filippov in this parametrization. Our proof shows that maximal causal curves are either everywhere lightlike or everywhere timelike. Furthermore, the proof demonstrates that maximal causal curves for an $alpha$-Holder continuous Lorentzian metric admit a $mathcal{C}^{1,frac{alpha}{4}}$-parametrization.



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