关于体积时间函数的可微性
On differentiability of volume time functions
摘要：
证明了整体双曲流形上一类Geroch体积函数的可微性。进一步证明了因果曲线上的每一个体积函数都满足局部反Lipschitz条件，且局部反Lipschitz的局部Lipschitz时间函数可以一致地由具有类时梯度的光滑时间函数逼近.最后，我们证明了在稳定因果时空中，霍金的时间函数可以用具有类时梯度的光滑时间函数一致逼近。
英文摘要：
We show differentiability of a class of Geroch's volume functions on globally hyperbolic manifolds. Furthermore, we prove that every volume function satisfies a local anti-Lipschitz condition over causal curves, and that locally Lipschitz time functions which are locally anti-Lipschitz can be uniformly approximated by smooth time functions with timelike gradient. Finally, we prove that in stably causal spacetimes Hawking's time function can be uniformly approximated by smooth time functions with timelike gradient.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
