Timeline for Can a non-compact manifold become compact by cutting it?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 5, 2020 at 14:14 | comment | added | aceituna | @HJRW A MOTS $\Sigma$ is a "marginally outer trapped surface", i.e. a trapped surface $\Sigma$ in a spacelike Cauchy hypersurface $V$ of a spacetime on which the null mean curvature w.r.t. the outward normal of $\Sigma$ in $V$ vanishes. (So it builds on a whole lot of other definitions of general relativity.) | |
| Jan 5, 2020 at 12:09 | comment | added | HJRW | What does MOTS mean? Anyway, if I understood it correctly, the answer to your second, more specific, question is “no” — if $V$ is non-compact then neither is $\tilde V$, however you construct it. | |
| Jan 5, 2020 at 9:54 | comment | added | aceituna | Its the second part of the proof for a Variation of the Penrose singularity theorem, switching the condition that the Cauchy surface $V$ contains a trapped surface to $V$ contains a MOTS $\Sigma$ and additionally the generic condition holds on each future and past inextendible null geodesic normal to $\Sigma$. It's Theorem 3.2 from the paper "Topological censorship from the initial data point of view" from Eichmair, Galloway and Pollack. | |
| Jan 5, 2020 at 1:35 | comment | added | Anton Petrunin | Then you get a manifold with boundary (I assume you do not want it). Anyway, could you tell what do you need to prove with this trick (it might help). | |
| Jan 4, 2020 at 22:46 | comment | added | aceituna | I mean 2 copies glued together along just one of the boundaries instead of both? | |
| Jan 4, 2020 at 21:00 | comment | added | HJRW | If you used two copies the surface wouldn’t separate the resulting manifold. | |
| Jan 4, 2020 at 20:47 | history | asked | aceituna | CC BY-SA 4.0 |