Timeline for Conformal flatness FLRW
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27 events
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| Aug 23 at 3:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
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| Jun 27, 2022 at 23:13 | comment | added | Octaaf | Well, there is no time translation symmetry in expanding FLRW space in general. And the continuity equation does not prevent photons from being redshifted. But the point of my question is mathematical in the first place. | |
| Jun 27, 2022 at 17:59 | comment | added | Eletie | I disagree, constant curvature solutions are not the only physically allowed FLRW solutions. They just happen to have constant curvature. In the Florides paper he's studying them just for mathematics sake. The conservation constraint (continuity equation) is automatically satisfied for any FLRW solution, not just these constant curvature ones. | |
| Jun 27, 2022 at 17:49 | comment | added | Octaaf | This is somewhat speculative on my part, but seems the only possible conclusion if both statements are correct. | |
| Jun 27, 2022 at 17:38 | comment | added | Octaaf | @Eletie, true, all are conformally flat. But due to Florides, the actual solution set is limited to those 6 of constant curvature. All Florides uses is the FLRW metric. Hence there must be an implicit constraint in the FLRW metric (I would say conservation of energy) from which Florides arives at these 6. All others fail to satisfy this undefined implicit property, therefore cannot exist as FLRW solution, if Florides is correct. | |
| Jun 26, 2022 at 11:54 | comment | added | Eletie | There still seems to be some confusion here: there is no need for the FLRW metric to be expressed in static form for conformal flatness, because of the conformal factor. The Weyl tensor vanishes for all FLRW metrics, for arbitrary $a(t)$. Florides is looking at constant spacetime curvature solutions - there's no connection here. | |
| Jun 26, 2022 at 10:00 | comment | added | Octaaf | Expressible in static form is not the same as being static | |
| Jun 25, 2022 at 23:23 | comment | added | Eletie | Yes, that's fine. In point 1 when you say 'How I read this, is that it makes the FLRW metric expressible in static form' is the incorrect part. There's no link between conformal flatness and the staticity requirements in your item 2. | |
| Jun 25, 2022 at 23:04 | comment | added | Octaaf | Statement 2) above in the exact words of Florides: “It is shown that there are six, and only six, Robertson-Walker metrics which can be expressed in static form. They are precisely those Robertson-Walker metrics whose spacetime curvature is constant.” And these include, e.g., the expanding dS spacetime | |
| Jun 25, 2022 at 22:52 | comment | added | Octaaf | @Eletie I’m sorry, that’s not what the question says. | |
| Jun 25, 2022 at 21:24 | comment | added | Eletie | @Octaff I'm not sure where you're getting that FLRW needs to be static for conformal flatness? That isn't what Florides is claiming. E.g. the FLRW metric with constant spatial curvature in conformal coordinates has a timelike conformal killing vector, but not a normal timeline one. | |
| Jun 25, 2022 at 12:22 | comment | added | Kosm | @Yukterez good point. I guess I was thinking about Minkowski form specifically. | |
| Jun 25, 2022 at 11:58 | comment | added | Yukterez | The scale factor $\rm a$ can be time dependend in a static metric, but $\rm \dot{a}/a=H$ can not | |
| Jun 25, 2022 at 11:53 | comment | added | Kosm | 1. Whether an FLRW metric is static or not depends on the solution to Einstein equations. For example for inflation, the scale factor is time dependent | |
| Jun 25, 2022 at 10:31 | comment | added | Octaaf | @Eletie: indeed. Florides shows that, given Minkowski (or any other static representation of FLRW), the solution set of expanding FLRW spacetimes is restricted to Milne and (A)dS. The implicit statement seems the FLRW metric is a (energy) conservation equation, therefore, restricts what you can put into the stress energy tensor if space expands. | |
| Jun 25, 2022 at 10:24 | answer | added | Yukterez | timeline score: 0 | |
| Jun 25, 2022 at 9:40 | comment | added | Octaaf | @Yukterez, of course, but the statement of Florides is about the opposite: if expressible in static coordinates (the FLRW metric is conformal to Minkowski) then the FLRW metric can only be one of these 6. | |
| Jun 25, 2022 at 8:08 | comment | added | Eletie | You don't need staticity for conformal flatness | |
| Jun 24, 2022 at 19:03 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Jun 24, 2022 at 19:00 | comment | added | Yukterez | If $H$ is independend of $t$ like it is in the metrics you mentioned above you can use static coordinates, but if it is time dependend you can't | |
| S Jun 24, 2022 at 18:38 | review | First questions | |||
| Jun 24, 2022 at 18:54 | |||||
| S Jun 24, 2022 at 18:38 | history | asked | Octaaf | CC BY-SA 4.0 |