- #1
purakanui
- 10
- 0
Hi. Currently I am self-studying a book on general relativity (Introducing Einstein's Relativity by Ray D'Inverno), I am stuck trying to find a Killing Vector solution to the following problem.
ds^2 = (x^2)dx^2 + x(dy)^2
You can easily obtain the metric from the above.
Now the question is find all Killing Vector solutions of the metric.
I know to solve this the lie derivative must equal 0. ie
Covariant derivative of Xa with respect to b + the covariant derivative of Xb with respect to a = 0. (1)
The answer in the back is the partial derivative with respect to y. (del/del y).
Basically I get to expanding (1) so now there are christoffel symbols but don't know where to go from there.
Thanks,
Chris
ds^2 = (x^2)dx^2 + x(dy)^2
You can easily obtain the metric from the above.
Now the question is find all Killing Vector solutions of the metric.
I know to solve this the lie derivative must equal 0. ie
Covariant derivative of Xa with respect to b + the covariant derivative of Xb with respect to a = 0. (1)
The answer in the back is the partial derivative with respect to y. (del/del y).
Basically I get to expanding (1) so now there are christoffel symbols but don't know where to go from there.
Thanks,
Chris