Recently I attempted to compute the stress-energy tensor for the space that I guessed was shaped like an expansionary phase of our universe. That attempt is stuck. Before that I came across a modification to the Poincaré’s conformal map from Hyperbolic plane to the Euclidean half plane. The modification was merely to change the metric from:
In both spaces the model half plane was {(x, y) | y>0}. I wrote a program to plot geodesics based on the 2nd metric. Here is the hyperbolic pseudo metric picture explained here.
I want to understand the symmetries of the space with metric diag(1, −et, −et, −et) for −∞<t<∞. I think I show here that the metric diag(1/T2, −1/T2, −1/T2, −1/T2) for −∞<t<0 is isometric to the former.
This explores a generalization of a technique to model uniformly curved spaces.