Globally hyperbolic spacetimes-with-timelike-boundary $(\overline{M} = M \cup \partial M, g)$ are the natural class of spacetimes where regular boundary conditions (eventually asymptotic, if $\partial M$ is obtained by means of a conformal embedding) can be posed. $\partial M$ represents the naked singularities and can be identified with a part of the intrinsic causal boundary. Apart from general properties of $\partial M$, the splitting of any globally hyperbolic $(\overline{M},g)$ as an orthogonal product $\mathbb{R}\times \bar\Sigma$ with Cauchy slices-with-boundary $\{t\}\times \bar\Sigma$ is proved. This is obtained by constructing a Cauchy temporal function~$\tau$ with gradient $\nabla \tau$ tangent to $\partial M$ on the boundary. To construct such a~$\tau$, results on stability of both global hyperbolicity and Cauchy temporal functions are obtained. Apart from having their own interest, these results allow us to circumvent technical difficulties introduced by $\partial M$. The techniques also show that $\overline{M}$ is isometric to the closure of some open subset in a globally hyperbolic spacetime (without boundary). As a trivial consequence, the interior $M$ both splits orthogonally and can be embedded isometrically in some $\mathbb{L}^N$, extending so properties of globally spacetimes without boundary to a class of causally continuous ones.

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具有时间似边界的全局双曲时空的结构

具有双曲线时空边界的全局双时空$（\ overline {M} = M \ cup \ partial M，g）$是自然时空类，其中规则边界条件（最终渐近，如果$ \ partial M $通过可以提出保形嵌入的方法。$ \ partial M $表示裸奇奇点，可以用内在因果边界的一部分来标识。除了$ \ partial M $的一般属性外，将任何全局双曲$（\ overline {M}，g）$作为正交乘积$ \ mathbb {R} \ times \ bar \ Sigma $与Cauchy slices-进行拆分边界$ \ {t \} \ times \ bar \ Sigma $被证明。这是通过构造边界上与$ \部分M $相切的梯度\\ nabla \ tau $的柯西时间函数〜$ \ tau $来获得的。要构造这样的a〜$ \ tau $，获得了关于整体双曲和Cauchy时间函数稳定性的结果。除了拥有自己的兴趣之外，这些结果还使我们能够避免$ \部分M $引入的技术难题。该技术还表明，\\ overline {M} $与全局双曲时空中某些开放子集的闭合等距（无边界）。琐碎的结果是，内部的$ M $都正交分解，并且可以等距地嵌入到$ \ mathbb {L} ^ N $中，从而将全局时空的属性扩展为一类因果连续的时空。该技术还表明，\\ overline {M} $与全局双曲时空中某些开放子集的闭合等距（无边界）。琐碎的结果是，内部的$ M $都正交分解，并且可以等距地嵌入到$ \ mathbb {L} ^ N $中，从而将全局时空的属性扩展为一类因果连续的时空。该技术还表明，\\ overline {M} $与全局双曲时空中某些开放子集的闭合等距（无边界）。琐碎的结果是，内部的$ M $都正交分解，并且可以等距地嵌入到$ \ mathbb {L} ^ N $中，从而将全局时空的属性扩展为一类因果连续的时空。