Changes

: Relativity does imply that space as well as space-time are curved.  The observation of a flat universe does contradict what would be expected if Relativity were true.--[[User:Aschlafly|Andy Schlafly]] 10:03, 13 August 2010 (EDT)

: Relativity does imply that space as well as space-time are curved.  The observation of a flat universe does contradict what would be expected if Relativity were true.--[[User:Aschlafly|Andy Schlafly]] 10:03, 13 August 2010 (EDT)

:::: A trivial solution to Einsteins field equations for a vacuum can result in Minkowski spacetime. This is a 4D metric describing a pseudo-Riemannian manifold with no spatial curvature (i.e. flat). A requirement of GR is that in locally inertial frames (i.e. small enough regions of spacetime) we recover Minkowski spacetime. It's just that in GR the requirement of a locally Minkwoski spacetime does not always extend to a global case with curvature effects breaking down the notion of inertial frames for all observers. The observation of a flat Universe (spatial curvature parameter, K = 0 in the FLRW metric) is not in violation of GR and is a valid solution to Einsteins field equations (see e.g. Friedmanns Equations) and a prediction of models of inflationary cosmology whereby a rapid expansion in the early Universe drives the Universe towards a spatially flat solution, certainly within the observable Universe. Predictions from GR are still obeyed contrary to the comment "flat universe does contradict what would be expected if Relativity were true".

:::: A trivial solution to Einsteins field equations for a vacuum can result in Minkowski spacetime. This is a 4D metric describing a pseudo-Riemannian manifold with no spatial curvature (i.e. flat). A requirement of GR is that in locally inertial frames (i.e. small enough regions of spacetime) we recover Minkowski spacetime. It's just that in GR the requirement of a locally Minkwoski spacetime does not always extend to a global case with curvature effects breaking down the notion of inertial frames for all observers. This means that a flat spacetime is a valid prediction arising from General Relativity. The presence of matter will, generically, curve spacetime but certain models such as the FLRW models used in cosmology permit solutions that predict a spatially flat Universe under a given condition. It should also be noted that the FLRW models are not static and do change with time.

 

::::The observation of a flat Universe (spatial curvature parameter, K = 0 in the FLRW metric) is not in violation of GR and is a valid solution to Einsteins field equations (see e.g. Friedmanns Equations) and a generic prediction of models for inflationary cosmology whereby a rapid expansion in the early Universe drives the Universe towards a spatially flat solution, certainly within the observable Universe. Predictions from GR are still obeyed contrary to the comment "flat universe does contradict what would be expected if Relativity were true".

:::: I do not feel that the point in discussion is in any way a counterpoint to relativity. If other objections arise then perhaps this point would need to be further clarified so that any issues may be appropriately discussed? 15th August 2010

:::: I do not feel that the point in discussion is in any way a counterpoint to relativity. If other objections arise then perhaps this point would need to be further clarified so that any issues may be appropriately discussed? 15th August 2010