Killing Problem 1

1. Feb 3, 2007

astronomia84

Does anyone know how can find φ(x,y) (conformal function)
if $$\xi =(y,-x)$$ & $$\eta = (x,y)$$ is killing vectors
,for this metric $$ds^2 = \phi(x,y)(dx^2 +dy^2)$$

???

:rofl:

2. Feb 3, 2007

cristo

Staff Emeritus
Well, $\xi$ and $\eta$ will satisfy Killing's equation, so use this, and you should be able to find $\phi(x,y)$

3. Feb 3, 2007

astronomia84

thanks

thanks cristo
,something more ...

4. Feb 3, 2007

cristo

Staff Emeritus
Well, what is Killing's equation? (There are various equivalent forms; the one involving the Lie Derivative of the metric may be most useful here)

5. Feb 4, 2007

astronomia84

Thank For All

YOU CAN WRITE THE FIRST STEPS FOR THE PROBLEM...

6. Feb 4, 2007

coalquay404

If you need somebody to write down the first steps towards solving this, you're hardly in a position to be attempting to answer the question.

Look, it's quite simple: you're being asked to find an expression for a two-dimensional conformal factor $\phi(x,y)$. You are given the metric:

$g_{ij} = \phi(x,y)\delta_{ij}$

and you're also given two Killing vectors. In order to solve the problem, start by thinking about what Killing's equation is. If $\vec{\xi}$ is a Killing vector, and $\nabla$ is a connection, what is Killing's equation?

7. Feb 4, 2007

astronomia84

MY QUESTION IS NOT HOMEWORK.
MY FIRST POST IS HERE…
AND MOVED HERE.
I READ FOR MY EXAMINATIONS IN GENERAL RELATIVITY.
IF YOU CAN HELP ME ANSWER.I DO NOT REQUEST.

THANKS FOR ALL MY FRIENDS.

8. Feb 4, 2007

astronomia84

MY FIRST POST IS HERE…

Physics -->Special & General Relativity -->Killing Problem 1

9. Feb 4, 2007

coalquay404

Again, let me ask you the same question:

What is Killing's equation?