Timeline for convergence theory -> lorentzian geometry
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 6, 2011 at 2:23 | answer | added | Christina Sormani | timeline score: 3 | |
| Aug 28, 2011 at 20:39 | vote | accept | michael | ||
| Aug 28, 2011 at 20:39 | vote | accept | michael | ||
| Aug 28, 2011 at 20:39 | |||||
| Aug 28, 2011 at 16:00 | answer | added | Johan Noldus | timeline score: 3 | |
| Aug 25, 2011 at 22:57 | comment | added | michael | yes, in some sense due to the remark you've just noted he has to work with the "natural" 4d-riemannian metric constructed from the lorentzian metric and the time-function. It's more or less always the case in articles i know around this subject, you look at globally hyperbolic spacetimes and in some sense you reduce your problem to a problem a riemannian geometry. i was wondering if since these results advance had been made by geometers . | |
| Aug 25, 2011 at 22:22 | comment | added | Ken Knox | I know you have said that you are familiar with Anderson's work, but in section 5 of his paper "Cheeger-Gromov theory and applications to general relativity" (math.sunysb.edu/~anderson/cargese.pdf) he seems to indicate that this is basically an open problem, and describes why using a curvature bound without choosing coordinates can be unsatisfactory. Namely that he describes the non-compact class of "plane-fronted gravitational waves" that satisfy $|R|^2 = 0$. Of course it would also be nice to hear about newer, updated work if it exists. | |
| Aug 25, 2011 at 22:02 | comment | added | michael | oh yes, i know his work on lorentzian versions of gromov-hausdorff distances. i was in fact wondering if there exists paper in which cheeger type compactness results or for instance pinching theorems were applied to get interesting results on lorentzian geometry. | |
| Aug 25, 2011 at 21:25 | comment | added | Rbega | I'm far from an expert on this, but I believe articles by Johan Noldus are as good a place to start as any... | |
| Aug 25, 2011 at 20:32 | history | asked | michael | CC BY-SA 3.0 |