# Killing Problem 1

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:

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

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
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)

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... 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?

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?

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

Again, let me ask you the same question:

What is Killing's equation?