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center o bass
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In general relativistic spacetimes, convex neighbourhoods are guaranteed to exist. As a reminder: a convex neighbourhood ##U## is a neighbourhood ##U## such that for any two points ##p## and ##q## in U there exists a unique geodesic connecting ##p## and ##q## staying within ##U##.
With that established, does it somehow follow that within a small enough neighbourhood there exist a unique null-geodesic connecting them?
In this paper the author seem to deduce this in his Proposition 1 -- something that he uses to establish the existence of neighbourhoods for which one can assign coordinates to events by sending and receiving light signals.
With that established, does it somehow follow that within a small enough neighbourhood there exist a unique null-geodesic connecting them?
In this paper the author seem to deduce this in his Proposition 1 -- something that he uses to establish the existence of neighbourhoods for which one can assign coordinates to events by sending and receiving light signals.
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