- #1
Pacopag
- 197
- 4
Hi everyone;
I'm new to both PF and GR, so please bear with me if I'm not being very clear, or using standard syntax and such. Here is my question.
Given a vector v^a, the covariant derivative is defined as v^a _;b = v^a _,b + v^c GAMMA^a _bc.
(here I'm using ^ before upper indices and _ before lower indices).
The object I'm interested in now is v^a;b (where the whole thing a;b is upper). Is this called the contravariant derivative? Is there a similar definition in terms of the Christoffel symbol? or can we only obtain it from contracting v^a _;b with the metric? I can't seem to find the definition of this object in any books, and when I try to do my calculation via contraction with the metric, I'm getting the wrong answer.
Thanks.
I'm new to both PF and GR, so please bear with me if I'm not being very clear, or using standard syntax and such. Here is my question.
Given a vector v^a, the covariant derivative is defined as v^a _;b = v^a _,b + v^c GAMMA^a _bc.
(here I'm using ^ before upper indices and _ before lower indices).
The object I'm interested in now is v^a;b (where the whole thing a;b is upper). Is this called the contravariant derivative? Is there a similar definition in terms of the Christoffel symbol? or can we only obtain it from contracting v^a _;b with the metric? I can't seem to find the definition of this object in any books, and when I try to do my calculation via contraction with the metric, I'm getting the wrong answer.
Thanks.