Timeline for Diffeomorphism invariance and geodesic action
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| May 2, 2016 at 21:39 | vote | accept | Wooster | ||
| Apr 30, 2016 at 4:13 | answer | added | zzz | timeline score: 10 | |
| Apr 11, 2016 at 11:59 | history | edited | Wooster | CC BY-SA 3.0 |
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| Apr 11, 2016 at 11:50 | review | Close votes | |||
| Apr 26, 2016 at 3:01 | |||||
| Apr 11, 2016 at 11:44 | comment | added | Wooster | Are you saying that $g_{ab}(x)$ should just become $g_{ab}(y)$? There also seems to be an issue in Twistor's answer in that the new metric under an active diffeomorphism should be written in the same coordinate basis i.e. $dx$ and not $dX$. | |
| Apr 11, 2016 at 11:43 | comment | added | Wooster | Twistor's answer is great, however I'm really trying to understand the details of this in the particular case of the action and the difference between a diffeomorphism and an isometry (there is no talk of Killing fields in that answer), that's where I'm struggling. What do you mean by drag the metric along in this case? | |
| Apr 11, 2016 at 11:34 | comment | added | ACuriousMind♦ | See twistor's answer - in the active p.o.v. on coordinate changes, you have to drag the metric along the diffeomorphism and use the result as the metric after the new transformation. It maps geodesics in the old metric to geodesics in the new metric, but it is not an isometry of $(M,g)$ to itself like the diffeomorphisms generated by Killing fields are. | |
| Apr 11, 2016 at 11:32 | comment | added | ACuriousMind♦ | Possible duplicate of The Role of Active and Passive Diffeomorphism Invariance in GR | |
| Apr 11, 2016 at 10:51 | history | edited | Qmechanic♦ | CC BY-SA 3.0 |
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| Apr 11, 2016 at 10:46 | history | asked | Wooster | CC BY-SA 3.0 |