Timeline for On the causal structure of spacetimes: piecewise $C^1$, $C^k$ or $C^\infty$?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 5, 2019 at 14:20 | answer | added | Clemens Sämann | timeline score: 5 | |
| Jul 18, 2017 at 12:28 | comment | added | Nanashi No Gombe | @StefanWaldmann Who is O'Neill? Can you please provide a link to the reference? Thanks. | |
| Apr 13, 2017 at 18:20 | vote | accept | Stefan Waldmann | ||
| Apr 9, 2017 at 10:22 | answer | added | Igor Khavkine | timeline score: 9 | |
| Apr 9, 2017 at 7:45 | history | edited | Stefan Waldmann | CC BY-SA 3.0 |
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| Apr 9, 2017 at 3:37 | comment | added | Sebastian Goette | I see. Maybe you should add this in your question (for people like me who don't know the difference between causal and forward timelike). Anyway, the cone still has strictly convex cross-section, and I have the impression that a causal curve that is not a lightlike geodesic should be approximable by timelike $C^\infty$ curves. But I don't have a proof or reference for that unfortunately. | |
| Apr 8, 2017 at 16:35 | comment | added | Stefan Waldmann | @Sebastian: Hmmm. I'm not so sure about the open condition. For timelike curves, i.e. with tangents in the open forward light cone, this should be OK, but for causal ones? If they have tangents on the (boundary of the) lightcone, the usual smearing could tilt the tangent outside the lightcone into spacial directions. At least, I don't see that directly. It just wonders me that in the literature this is not discussed too well. The timelike curves are certainly robust enough. | |
| Apr 8, 2017 at 14:15 | comment | added | Sebastian Goette | Have you thought about approximating $C^k$ curves by $C^\ell$ curves for $\ell>k$? It seems to me that being causal is an open condition in $C^1$ topology and the forward timelike cone is convex at each point, so all this should be possible. In other words, the causal structure should be independent of the choice. Or am I missing some important point here? | |
| Apr 8, 2017 at 10:39 | history | asked | Stefan Waldmann | CC BY-SA 3.0 |