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Space Curvature - Discussion Poster

March 2019

Authors:

Aleksandar Janjic

Technical University of Munich

In accordance with Friedmann-Lemaitre-Equation there are three different possibilities of space curvature which can be described mathematically and imparted graphically or analogously (Closed, Openend or Flat Universe). In the attached poster a fourth graphic representation is shown, which is however only graphically derived. Is this sketch describable within Friedmann-Lemaitre-Equations? How can we interpret this sketch? A Universe that is truly infinite, although it has a defined start and a defined end point? What would be a 3-Dimensional mathematical object to describe the plot (closed hypertorus, while closed means without a connection in the center?). And what numbers for curvature parameter k and density Parameter Ω make sense for this sketch? I have created this plot purely graphically and wonder whether a mathematical interpretation of such a shaped space-time is possible, or whether it inevitably leads to paradoxes and is thus a graphic that can be drawn abstractly, but ultimately makes no mathematical sense.

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