Timeline for A question on light cones in Lorentzian manifolds with timelike boundary
Current License: CC BY-SA 4.0
7 events
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| May 29, 2021 at 6:13 | history | edited | Pedro Lauridsen Ribeiro | CC BY-SA 4.0 |
Partial completion of answer in view of previously missing information from the question
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| May 29, 2021 at 4:34 | comment | added | Pedro Lauridsen Ribeiro | In fact, I misread the end of your question - I missed the part where $S$ is the boundary of a spacelike hypersurface $\Sigma$ in $M$. However, I think one can complete my answer in order to comtemplate that as well using the global time function $(t,p)\mapsto t$ in $M$ ($p\in M_0$). I'll amend my answer shortly. | |
| May 29, 2021 at 4:30 | comment | added | Pedro Lauridsen Ribeiro | "Spacelike" and "acausal" are different things - "spacelike" means that the tangent bundle of $S$ consists only of spacelike tangent vectors, whereas "acausal" means there is no causal curve in $M$ linking two different points of $S$. One does not imply the other - the example I gave in the first paragraph of my answer shows that an acausal hypersurface can have nonspacelike tangent vectors. | |
| May 29, 2021 at 3:33 | comment | added | Ali | It seems to me that you show that S is spacelike. Does this obviously imply that there is a spacelike surface whose boundary is S? | |
| May 29, 2021 at 0:16 | vote | accept | Ali | ||
| May 28, 2021 at 22:38 | history | edited | Pedro Lauridsen Ribeiro | CC BY-SA 4.0 |
Added remark
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| May 28, 2021 at 22:21 | history | answered | Pedro Lauridsen Ribeiro | CC BY-SA 4.0 |