The forum discussion focuses on deriving a function that expresses redshift as a function of distance modulus (DM) in an empty universe model (Omega=0). Users share resources, including type 1A supernova data from UCLA and relevant academic papers, to assist in plotting the Omega=0 curve. The conversation delves into the implications of closed and open universes, discussing concepts such as spatial curvature, the nature of manifolds in General Relativity, and the potential for closed timelike curves in compact Lorentzian manifolds.
PREREQUISITESAstronomers, cosmologists, and physics students interested in the mathematical modeling of the universe, particularly those exploring the implications of different cosmological models and the nature of spacetime.
George Jones said:All compact 4-dimensional Lorentzian manifolds have closed timelike curves
Well, the arrow of time is most likely a local property, but that doesn't make closed timelike curves any more sensible.Imax said:Maybe time orientable is a locale property, which may not necessarily exclude the possibility of closed timelike geodesics?
Chalnoth said:Well, the arrow of time is most likely a local property, but that doesn't make closed timelike curves any more sensible.
Well, a compact Lorentzian manifold has closed timelike curves. That's one reason why our universe isn't one.Imax said:If we asume that the arrow of time is a local property within a compact Lorentzian manifold, then closed timelike geodesics may be alllowed, and events could repeat.
Chalnoth said:Well, a compact Lorentzian manifold has closed timelike curves. That's one reason why our universe isn't one.