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Yes, it should be possible. You can find an example in this notebook.

It's done by defining the initial 4-velocity with a negative time component (cells 26-27 in the example).

You didn't post your full code I can't be completely sure, but my guess is that the integration parameter inside integrated_geodesic is expected to be increasing. ​Could you try to replace the second line in your code with

​geod = M.integrated_geodesic(g, (s, 0, 50), -v0, across_charts=True)

It's a bit of a workaround, but it should work. I didn't expect people to call solve_across_charts in this way, but it's in fact logical. I think we should support it (or at least throw an error when declaring the geodesic). It's probably just a matter of adding some absolute values in some places, and maybe fixing the chart limit detection.