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Killing Problem 1

  1. Feb 3, 2007 #1
    Does anyone know how can find φ(x,y) (conformal function)
    if [tex] \xi =(y,-x) [/tex] & [tex] \eta = (x,y) [/tex] is killing vectors
    ,for this metric [tex]ds^2 = \phi(x,y)(dx^2 +dy^2) [/tex]

    ???

    o:) :rofl:
     
  2. jcsd
  3. Feb 3, 2007 #2

    cristo

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    Well, [itex]\xi[/itex] and [itex]\eta[/itex] will satisfy Killing's equation, so use this, and you should be able to find [itex]\phi(x,y)[/itex]
     
  4. Feb 3, 2007 #3
    thanks

    thanks cristo
    ,something more ...
    :biggrin:
     
  5. Feb 3, 2007 #4

    cristo

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    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)
     
  6. Feb 4, 2007 #5
    Thank For All



    YOU CAN WRITE THE FIRST STEPS FOR THE PROBLEM...
    :blushing:
     
  7. Feb 4, 2007 #6
    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 [itex]\phi(x,y)[/itex]. You are given the metric:

    [itex] g_{ij} = \phi(x,y)\delta_{ij}[/itex]

    and you're also given two Killing vectors. In order to solve the problem, start by thinking about what Killing's equation is. If [itex]\vec{\xi}[/itex] is a Killing vector, and [itex]\nabla[/itex] is a connection, what is Killing's equation?
     
  8. Feb 4, 2007 #7
    answer---answer


    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.
    :bugeye: :bugeye: :bugeye:
    THANKS FOR ALL MY FRIENDS.
     
  9. Feb 4, 2007 #8
    MY FIRST POST IS HERE…

    Physics -->Special & General Relativity -->Killing Problem 1
     
  10. Feb 4, 2007 #9
    Again, let me ask you the same question:

    What is Killing's equation?
     
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