Timeline for Necessary and sufficient conditions for pseudo Riemannian manifold to be time orientable
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Apr 9, 2023 at 20:13 | history | bounty ended | Chris | ||
| S Apr 9, 2023 at 20:13 | history | notice removed | Chris | ||
| Apr 2, 2023 at 21:52 | vote | accept | Chris | ||
| Apr 2, 2023 at 21:51 | answer | added | Ryan Budney | timeline score: 1 | |
| Apr 2, 2023 at 21:46 | comment | added | Chris | @RyanBudney I see that makes sense. If you would like to expand on your comment with an answer I will award it the bounty | |
| Apr 2, 2023 at 21:39 | comment | added | Ryan Budney | Right, your first paragraph, but adapted to the decomposition $TM \simeq E^t \oplus E^s$. This decomposition you get by arguing that the full-rank timelike (or spacelike) subspaces of a vector space with non-degenerate symmetric bilinear form, they are a convex space. So you piece together the decomposition of the tangent bundle fibrewise, with a partition of unity argument. | |
| Apr 2, 2023 at 21:34 | comment | added | Chris | @RyanBudney Ok, so that's pretty much what I said in the my last paragraph? | |
| Apr 2, 2023 at 21:33 | comment | added | Ryan Budney | Hi Chris, but I think it's the exact same argument. You have a Stiefel-Whitney class for each sub-bundle, the first sub-bundle is orientable if the $w_1$ class for that sub-bundle is trivial. The 2nd is orientable if its $w_1$ class is trivial. So if I understand which notion of orientability you are interested in, it would be the one for the timelike subspace, i.e. you want a timelike sense of direction. | |
| Apr 2, 2023 at 21:01 | comment | added | Chris | @RyanBudney I don't think this is covered in Whiston's paper. He does not really mention time orientability in depth out side of the $(1,3)$ case | |
| Apr 2, 2023 at 20:09 | comment | added | Chris | @RyanBudney was unaware of this paper, but I’ll check it out | |
| Apr 2, 2023 at 20:05 | comment | added | Ryan Budney | Isn't this covered in George Whiston's paper "Lorentzian characteristic classes" GRG (1975)? | |
| S Apr 2, 2023 at 18:36 | history | bounty started | Chris | ||
| S Apr 2, 2023 at 18:36 | history | notice added | Chris | Draw attention | |
| Mar 31, 2023 at 18:07 | history | asked | Chris | CC BY-SA 4.0 |