On 2/19/2019 3:41 AM, [email protected] wrote:
*I don't understand your comment. Curvature of space-time should be independent of coordinate systems, so how can there be different extremals for two fixed events in the manifold? AG*
There can be a "hill" between the two events so that there are extremal paths around it, one on each side. This how a galactic mass produces Einstein's ring. A common test question is: There is a clock in low Earth orbit. Another clock is launched straight up (assume non-rotating Earth) so that it just passes the orbiting clock on the way up and then it falls back such that it just passes the orbiting clock, one orbit later, on it's way down. Between the two coincident events the clocks are in free fall, following geodesics. Which one registers the longer interval between the coincident events?
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