Find φ(x,y) Using Killing Vectors: Conformal Function

[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 $$ds^2 = \phi(x,y)(dx^2 +dy^2)$$

?

 

[cristo]

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

 

[astronomia84]

thanks

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

thanks cristo
,something more ...

 

[cristo]

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)

 

[astronomia84]

Thank For All

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)

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

 

[coalquay404]

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

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?

 

[astronomia84]

answer---answer

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?

MY QUESTION IS NOT HOMEWORK.
MY FIRST POST IS HERE…
https://www.physicsforums.com/showthread.php?t=154436
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.

 

[astronomia84]

MY FIRST POST IS HERE…

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

 

[coalquay404]

Again, let me ask you the same question:

What is Killing's equation?