Metric tensor - index manipulation

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The discussion centers on the manipulation of the metric tensor and whether a specific index operation is valid. The original poster questions the legitimacy of their calculation involving the metric tensor components. A response indicates that the proposed manipulation is not permissible and asks for clarification on the context. The poster reveals that their inquiry is linked to solving a problem from MTW Ex 19.2, specifically regarding the ij0 component of the Christoffel Symbol with a zero time derivative of gij. The exchange highlights the complexities involved in tensor calculus and the importance of proper index manipulation.
zn5252
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hello,
Do I have the right to perform the following :

gjo,i + g0i,j = (gj0 δij + g0i ),j = (2 g0i ),j

Thank you,
Clear skies,
 
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No you can't do that. What is it you are trying to do in context?
 
I see. this is related to my attempt to solving MTW Ex 19.2 where I need to find the ij0 component of the Christoffel Symbol with a zero time derivative of the gij.
 

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