# 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?