- #1
Magister
- 83
- 0
Hi
Solving a Killing vector problem, in General Relativity, I got the following PDE system:
[tex]
\frac{\partial X^0}{\partial x}=0
[/tex]
[tex]
\frac{\partial X^1}{\partial y}=0
[/tex]
[tex]
\frac{\partial X^2}{\partial z}=0
[/tex]
[tex]
\frac{\partial X^0}{\partial y} + \frac{\partial X^1}{\partial x}=0
[/tex]
[tex]
\frac{\partial X^0}{\partial z} + \frac{\partial X^2}{\partial x}=0
[/tex]
[tex]
\frac{\partial X^1}{\partial z} + \frac{\partial X^2}{\partial y}=0
[/tex]
where [itex] X^a , a=0,1,2[/itex] are the three components of the Killing vector that I am looking for. I have spend a lot of time trying to solve this system but I am not getting any solution.
Thanks for any idea.
Solving a Killing vector problem, in General Relativity, I got the following PDE system:
[tex]
\frac{\partial X^0}{\partial x}=0
[/tex]
[tex]
\frac{\partial X^1}{\partial y}=0
[/tex]
[tex]
\frac{\partial X^2}{\partial z}=0
[/tex]
[tex]
\frac{\partial X^0}{\partial y} + \frac{\partial X^1}{\partial x}=0
[/tex]
[tex]
\frac{\partial X^0}{\partial z} + \frac{\partial X^2}{\partial x}=0
[/tex]
[tex]
\frac{\partial X^1}{\partial z} + \frac{\partial X^2}{\partial y}=0
[/tex]
where [itex] X^a , a=0,1,2[/itex] are the three components of the Killing vector that I am looking for. I have spend a lot of time trying to solve this system but I am not getting any solution.
Thanks for any idea.
Last edited: