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 Exercise [19.16] c 
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Joined: 12 Jul 2010, 07:44
Posts: 154
Post Exercise [19.16] c
My solution is entirely different to Roberto's (or Laura's).

I think they've both missed the key relationship between time-evolution and Lie derivatives, namely that "D" here is just -\pounds_t; i.e. that the time evolution of a volume is found by "dragging" it along the \frac{d}{d\tau} vector field (where \tau = proper time)!

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29 Apr 2012, 08:40

Joined: 12 Jul 2010, 07:44
Posts: 154
Post Re: Exercise [19.16] c
Note that in the next chapter, on p.484 and in exercise [20.15], the evolution of a volume element is explicitly stated to be its Lie derivative with respect to time (albeit in a rather different context).

18 May 2012, 08:37
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