论文标题
洛伦兹遇到了利普奇兹
Lorentz meets Lipschitz
论文作者
论文摘要
我们表明，Lipschitz连续的Lorentzian Metric的最大因果曲线接纳了$ \ Mathcal {C}^{1,1} $ - 参数化，并且它们在此参数化中以Filippov的意义求解了地质方程。我们的证明表明，最大因果曲线要么在任何地方。此外，证明证明了$α$-Hölder连续的Lorentzian Metric的最大因果曲线允许$ \ Mathcal {C}^{1，\fracα{4}} $ -Amartetrization。
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 $α$-Hölder continuous Lorentzian metric admit a $\mathcal{C}^{1,\fracα{4}}$-parametrization.
