Dear all,
In my journey through learning General relativity. I have stumbled upon this problem. I have to calculate the geodesic equation for R[itex]^{3}[/itex] in cylindrical polars. I am not sure how to use the metric connection. The indices confuse me. I would appreciate it if someone could shade some light on it. Every time I try to calculate it I get zero, sometimes due to the first metric tensor and sometime the terms in the parentheses are zeros.
[itex]\Gamma_{bc}^{a}=\frac{1}{2}g^{ad}(\partial_{b}g_{dc}+\partial_{c}g_{db}-\partial_{d}g_{bc})[/itex]
As I understand it, the index d is the dummy index and runs from 1 to 3 in this case, right? What about b and c? how do I use them?
Thanks in advance
In my journey through learning General relativity. I have stumbled upon this problem. I have to calculate the geodesic equation for R[itex]^{3}[/itex] in cylindrical polars. I am not sure how to use the metric connection. The indices confuse me. I would appreciate it if someone could shade some light on it. Every time I try to calculate it I get zero, sometimes due to the first metric tensor and sometime the terms in the parentheses are zeros.
[itex]\Gamma_{bc}^{a}=\frac{1}{2}g^{ad}(\partial_{b}g_{dc}+\partial_{c}g_{db}-\partial_{d}g_{bc})[/itex]
As I understand it, the index d is the dummy index and runs from 1 to 3 in this case, right? What about b and c? how do I use them?
Thanks in advance
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