Covariant derivative of the metric

hello!
just a quick question, does the covariant derivative of the metric give zero even when the indices(one of the indices) of the metric are(is) raised?
also another question not entirely related, does the covariant deriv. of exp(2 phi) where phi is the field, also give zero or not necessarily? thanks
 

haushofer

Science Advisor
Insights Author
2,227
562
Act with the covariant derivative on a kronecker delta. You know that

[tex]
g_{ab}g^{bc} = \delta_a^c
[/tex]

The covariant derivative of your exponential of scalar field is given by a partial derivative per definition; this will only be zero for constant phi.
 
if u act on a kronecker delta with the covariant deriv will that give zero? :S
 

haushofer

Science Advisor
Insights Author
2,227
562
Well, you know how a covariant derivative acts on a (1,1)-type tensor, right? Just write it down explicitly and check :) I would say that you'll find that it indeed is zero, provided the connection is symmetric.
 

Related Threads for: Covariant derivative of the metric

Replies
3
Views
12K
Replies
5
Views
3K
Replies
1
Views
4K
Replies
6
Views
1K
Replies
3
Views
3K
  • Posted
Replies
1
Views
2K
  • Posted
Replies
1
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top