Question: How to plot the geodesics from a simple metric



DGsetup([x, t], M1);

g := evalDG((dt &t dt) - t^2*(dx &t dx))


I created a two dimensional cross-section of a spacetime described by this metric above. 

I would like to plot the geodesics in polar coordinates using the time t as the radius (normalized to our current time equal to unity).

That is, I would like to plot the geodesics starting at x=0, t=1 (x=0 maps to the top of the polar plot). X is the polar angle.

This plot is likely to map to this figure. Never mind the details of wiggles, or titles, etc.  I am new to maple and could use an initial push.

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