Endless geodesics in closed spacetime

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SUMMARY

A closed spacetime can indeed contain an infinite number of geodesics with infinite length, as demonstrated in discussions surrounding general relativity and cosmological models. The presence of mass-energy curvature in a closed universe influences local curvature, leading to the conclusion that interior photons may ultimately be directed toward a singularity. This phenomenon highlights the complex interplay between geometry and physics in closed universes.

PREREQUISITES
  • Understanding of general relativity principles
  • Familiarity with geodesics in differential geometry
  • Knowledge of singularities in cosmological models
  • Basic concepts of mass-energy curvature
NEXT STEPS
  • Research the implications of geodesics in closed universes using general relativity
  • Explore the role of singularities in cosmological models
  • Study the mathematical formulation of geodesics in differential geometry
  • Investigate the effects of mass-energy curvature on spacetime geometry
USEFUL FOR

The discussion is beneficial for theoretical physicists, cosmologists, and students of general relativity interested in the properties of closed spacetimes and their implications for the universe's structure.

Loren Booda
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Can you show that a closed spacetime may embody one (or even an infinity of) geodesics with infinite length? How does this influence local curvature?
 
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That is, can a closed universe contain a geodesic infinite in length?

(I assume that the mass-energy curvature of a closed universe would eventually lead any interior photon to a singularity.)
 

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