Line element for the Gödel metric with all terms shown

[space-time]

Can someone please type out the line element for the Godel metric (including any and all c terms and any other terms that one might omit if they were using natural units to set terms like c = 1)? I ask this because different sources on line have it written out in different ways which look somewhat sloppy and hard for me to understand. With the latex here, we have access to more advanced mathematical symbols for typing as well as superscripts and subscripts (which will make it easier to read).

Thank you in advance.

 

[Mentz114]

It is here http://en.wikipedia.org/wiki/G%C3%B6del_metric.[/PLAIN]

Put a factor of $c$ in front of $dt$.

$ds^2= \frac{1}{2\omega^2} [ -(c\ dt + e^x dz)^2 + dx^2 + dy^2 + \tfrac{1}{2} e^{2x} dz^2], \qquad\qquad -\infty < t,x,y,z < \infty$

 

[space-time]

It is here http://en.wikipedia.org/wiki/G%C3%B6del_metric.[/PLAIN]

Put a factor of $c$ in front of $dt$.

$ds^2= \frac{1}{2\omega^2} [ -(c\ dt + e^x dz)^2 + dx^2 + dy^2 + \tfrac{1}{2} e^{2x} dz^2], \qquad\qquad -\infty < t,x,y,z < \infty$

Thank you