Timeline for On the causal structure of spacetimes: piecewise $C^1$, $C^k$ or $C^\infty$?
Current License: CC BY-SA 3.0
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| May 30, 2017 at 10:12 | comment | added | Igor Khavkine | @StefanWaldmann, the earliest relevant reference that I know from the classic literature on causality theory is Prop 2.19 of Techniques of differential topology in Relativity by R. Penrose (SIAM, 1972). Penrose proves that two points connected by a "broken" null geodesic are either connected by a single "unbroken" null geodesic or by a "broken" timelike geodesic. Since the individual pieces of these "broken" curves are all geodesics, their regularity is dictated by the regularity of the metric. | |
| Apr 13, 2017 at 18:20 | vote | accept | Stefan Waldmann | ||
| Apr 9, 2017 at 11:21 | comment | added | Igor Khavkine | For the record, I think for regular metrics the actual results of this sort are rather old. The article [C] from 2011 is a review, which was conveniently time with respect to the actual novel results of [CG] about rough metrics. | |
| Apr 9, 2017 at 10:59 | comment | added | Stefan Waldmann | Thanks a lot. I will take a look at the references. In any case, I'm happy that this seems to be not completely innocent (the paper being of 2011...). | |
| Apr 9, 2017 at 10:22 | history | answered | Igor Khavkine | CC BY-SA 3.0 |