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Ibix

Science Advisor

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Carroll develops Kruskal-Szekeres coordinates starting as a transformation from Schwarzschild exterior coordinates. I was thinking of picking a different zero for the original Schwarzschild coordinate time and repeating the same development, which generates boosted coordinates (so I should have said "different Schwarzschild coordinate time origin"). Transporting along the KVF that's not associated with spherical symmetry is a better and coordinate free description of that, yes.PeterDonis said:I'm not sure "pick a different time origin" is the correct way to describe what is being done.

And I agree your point that unlike the origin of Einstein ##x-t## coordinates on Minkowski spacetime, the choice of origin of K-S ##X-T## coordinates is not free - it's got to lie on the center of the spherical symmetry and half way between the singularities. And that is a sphere and not an event, as you say - in fact, it's the neck of the wormhole at its maximum radius, as discussed earlier. The boost freedom is just a freedom to pick which direction from an event on that sphere that we call the ##X## axis, analogous to the freedom to pick a zero meridian (through Greenwich or Paris or whatever) on the Earth.

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