洛伦兹和利普希兹相遇

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2020-09-18 DOI:10.4310/ATMP.2021.v25.n8.a4
Christian Lange, A. Lytchak, Clemens Samann
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引用次数: 9

摘要

我们证明了Lipschitz连续洛伦兹度规的最大因果曲线允许$\mathcal{C}^{1,1}$ -参数化,并在该参数化中解出了Filippov意义上的测地方程。我们的证明表明,最大因果曲线要么处处是类光曲线,要么处处是类时曲线。进一步证明了$\alpha$ -Holder连续洛伦兹度量的最大因果曲线允许$\mathcal{C}^{1,\frac{\alpha}{4}}$ -参数化。
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Lorentz Meets Lipschitz
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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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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