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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJul 22nd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have split off a stub [[globally hyperbolic Lorentzian manifold]] from [[Cauchy surface]]

   I have split off a stub globally hyperbolic Lorentzian manifold from Cauchy surface

2. • CommentRowNumber2.
   • CommentAuthorTobyBartels
   • CommentTimeJul 23rd 2011
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexWow, I didn't realise that the definition of globally hyperbolic was so simple!

   Wow, I didn’t realise that the definition of globally hyperbolic was so simple!

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJul 23rd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItex> Wow Yes, it is surprising that this is not advertized more widely. I have now added pointers to the theorems that establish this.

   Wow

   Yes, it is surprising that this is not advertized more widely.

   I have now added pointers to the theorems that establish this.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 23rd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have expanded the discussion a bit more.

   I have expanded the discussion a bit more.

5. • CommentRowNumber5.
   • CommentAuthorTobyBartels
   • CommentTimeJul 23rd 2011
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexThis theorem means that something that I wrote at [[Cauchy surface]] is not true; I fixed it in such a way as to link to [[globally hyperbolic]] (again) there.

   This theorem means that something that I wrote at Cauchy surface is not true; I fixed it in such a way as to link to globally hyperbolic (again) there.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJul 23rd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexCurrently the entry says that global hyperbolicity of $X$ implies the existence of a homeomorphism $\mathbb{R} \times \Sigma \to X$ that exhibits the foliation by Cauchy surfaces. I should check: can we not assume that this is a diffeomorphism with respect to the canonical smooth structure? I don't have more time for this right now. Maybe somebody knows directly? Otherwise I'll try to check later.

   Currently the entry says that global hyperbolicity of $X$ implies the existence of a homeomorphism $\mathbb{R} \times \Sigma \to X$ that exhibits the foliation by Cauchy surfaces.

   I should check: can we not assume that this is a diffeomorphism with respect to the canonical smooth structure?

   I don’t have more time for this right now. Maybe somebody knows directly? Otherwise I’ll try to check later.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeDec 21st 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * E. Minguzzi, [[Miguel Sánchez]], §3.11 in: *The causal hierarchy of spacetimes*, in: *Recent Developments in Pseudo-Riemannian Geometry*, EMS ESI Lectures in Mathematics and Physics **4** (2008) 299-358 &lbrack;[arXiv:gr-qc/0609119](https://arxiv.org/abs/gr-qc/0609119), [ISBN:978-3-03719-051-7](https://bookstore.ams.org/view?ProductCode=EMSESILEC/4)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/globally+hyperbolic+Lorentzian+manifold/13">diff</a>, <a href="https://ncatlab.org/nlab/revision/globally+hyperbolic+Lorentzian+manifold/13">v13</a>, <a href="https://ncatlab.org/nlab/show/globally+hyperbolic+Lorentzian+manifold">current</a>

   added pointer to:

   • E. Minguzzi, Miguel Sánchez, §3.11 in: The causal hierarchy of spacetimes, in: Recent Developments in Pseudo-Riemannian Geometry, EMS ESI Lectures in Mathematics and Physics 4 (2008) 299-358 [arXiv:gr-qc/0609119, ISBN:978-3-03719-051-7]

   diff, v13, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeDec 21st 2023
   • (edited Dec 21st 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexalso pointer to: * [[Miguel Sánchez]], *Globally hyperbolic spacetimes: slicings, boundaries and counterexamples*, Gen Relativ Gravit **54** 124 (2022) &lbrack;[arXiv:2110.13672](https://arxiv.org/abs/2110.13672), [doi:10.1007/s10714-022-03002-6](https://doi.org/10.1007/s10714-022-03002-6)&rbrack; * [[Antonio N. Bernal]], [[Miguel Sánchez]], *Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes*, Commun. Math. Phys. **257** (2005) 43-50 &lbrack;[arXiv:gr-qc/0401112](https://arxiv.org/abs/gr-qc/0401112), [doi:10.1007/s00220-005-1346-1](https://doi.org/10.1007/s00220-005-1346-1)&rbrack; * [[Antonio N. Bernal]], [[Miguel Sánchez]], *Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions*, Lett. Math. Phys. **77** (2006) 183-197 &lbrack;[arXiv:gr-qc/0512095](https://arxiv.org/abs/gr-qc/0512095), [doi:10.1007/s11005-006-0091-5](https://doi.org/10.1007/s11005-006-0091-5)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/globally+hyperbolic+Lorentzian+manifold/13">diff</a>, <a href="https://ncatlab.org/nlab/revision/globally+hyperbolic+Lorentzian+manifold/13">v13</a>, <a href="https://ncatlab.org/nlab/show/globally+hyperbolic+Lorentzian+manifold">current</a>

   also pointer to:

   • Miguel Sánchez, Globally hyperbolic spacetimes: slicings, boundaries and counterexamples, Gen Relativ Gravit 54 124 (2022) [arXiv:2110.13672, doi:10.1007/s10714-022-03002-6]

   • Antonio N. Bernal, Miguel Sánchez, Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes, Commun. Math. Phys. 257 (2005) 43-50 [arXiv:gr-qc/0401112, doi:10.1007/s00220-005-1346-1]

   • Antonio N. Bernal, Miguel Sánchez, Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions, Lett. Math. Phys. 77 (2006) 183-197 [arXiv:gr-qc/0512095, doi:10.1007/s11005-006-0091-5]

   diff, v13, current