Killing Problem 1

  • #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:
 

Answers and Replies

  • #2
cristo
Staff Emeritus
Science Advisor
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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]
 
  • #3
thanks

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]
thanks cristo
,something more ...
:biggrin:
 
  • #4
cristo
Staff Emeritus
Science Advisor
8,107
73
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
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...
:blushing:
 
  • #6
216
1
YOU CAN WRITE THE FIRST STEPS FOR THE PROBLEM...
:blushing:
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?
 
  • #7
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 [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?

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.
 
  • #8
MY FIRST POST IS HERE…

Physics -->Special & General Relativity -->Killing Problem 1
 
  • #9
216
1
Again, let me ask you the same question:

What is Killing's equation?
 

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