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 Notation Nabla^a in section 19.5 
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Joined: 21 Jul 2008, 04:37
Posts: 6
Post Notation Nabla^a in section 19.5
In the expression of the energy-momentum tensor conservation equation, we see Nabla^a. I am wondering if the superscript here means anything different from the subscript version Nabla_a, since I couldn't find a reasonable way to interpret the superscript version as an index-raised version of the subscript version via the metric g_ab.


15 Aug 2008, 02:11

Joined: 13 Mar 2008, 14:06
Posts: 42
Location: Ithaca NY
Post Re: Notation Nabla^a in section 19.5
yunjiangster wrote:
In the expression of the energy-momentum tensor conservation equation, we see Nabla^a. I am wondering if the superscript here means anything different from the subscript version Nabla_a, since I couldn't find a reasonable way to interpret the superscript version as an index-raised version of the subscript version via the metric g_ab.

The index-raised version is exactly what it is, and you don't have to interpret anything. Just calculate it. \nabla^a=g^{ab}\nabla_b
Laura


16 Sep 2008, 23:15

Joined: 26 Mar 2010, 04:39
Posts: 109
Post Re: Notation Nabla^a in section 19.5
As an additional point, notice that the metric commutes with the covariant derivative so it doesn't matter which way round you write this. For example:


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06 Jul 2010, 05:53
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