The forum discussion centers on the transition from a square-based lattice of geodesics to a circular-based lattice in the context of General Relativity (GR). Participants emphasize that mass cannot spontaneously appear from a mass-free state, as this would violate the principles of local energy conservation inherent in GR. They clarify that while energy densities can influence spacetime curvature, a direct transformation from flat to curved spacetime without mass or energy input is not feasible. The discussion 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 permissible in classical GR.
PREREQUISITESThis discussion is beneficial for physicists, students of theoretical physics, and anyone interested in the intricacies of General Relativity and the mathematical foundations of spacetime geometry.
Ok, I just thought that would have been one possible reason for believing that a linear geodesic could turn into a circular one.DaTario said:Yes, Dale, I am aware of this fact. It is like the extended parabola I presented in #25 (not the 2D 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.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.