I just noticed a few typos in the above. Throughout the t's should be ##\tau##'s, theyre the proper time of the observer. Also ##u^{t}=\frac{1}{2a}## not ##\frac{1}{\sqrt{2}a}##. I already made one edit, and apparently I can't make more so I'll post this here.
Also, if I try to evaluate...
Homework Statement
Consider the Godel Metric in spherical coordinates as on page 6 here;
ds^2=4a^2\left[-dt^2+dr^2+dz^2-(\sinh^{4}(r)-\sinh^{2}(r))d\phi^2+2\sqrt{2}\sinh^{2}(r)dt d\phi)\right]
This is a solution to Einstein's Equations if we have ##a=\frac{1}{2\sqrt{2\pi\rho}}## and ##\Lambda...