I How can a square-based lattice turn into a circular-based one?

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The discussion centers on the transition from a square-based lattice of geodesics in flat space to a circular-based lattice around a mass, questioning how such a transformation occurs within the framework of general relativity (GR). Participants emphasize that GR prohibits the creation of mass from empty space, as this would violate local conservation laws. They clarify that energy densities can influence spacetime curvature, but a direct transition from flat to curved spacetime without mass or energy present is not feasible. The conversation also touches on the fixed topology of spacetime in GR, asserting that a straight line cannot become a circle without a change in topology, which is not supported by classical GR. Ultimately, the need for better foundational understanding of GR is highlighted, suggesting that the original inquiry stems from misconceptions about the theory.
  • #31
DaTario said:
Yes, Dale, I am aware of this fact. It is like the extended parabola I presented in #25 (not the 2D one).
Ok, I just thought that would have been one possible reason for believing that a linear geodesic could turn into a circular one.
 
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  • #32
Dale said:
Ok, I just thought that would have been one possible reason for believing that a linear geodesic could turn into a circular one.
Thank you, Dale. This comment of yours was enlightening. So, it seems that we can say that there are no circular geodesics, at least as long as no time travel is considered.
If this is the case, then it could have been a nice answer to my question.
 

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