Changes

[[Curvature of spacetime]] (singular as opposed to plural "curvatures") is something that describes a fact that some 4-dimensional space is curved. It can't happen though in a stationary universe since the [[spacetime]] of stationary universe has to be flat (or [[Minkowski]], which is another word for the same thing). In particular '''curvatures of spacetime''' may describe the curvature of the common 3-dimenssional space (given by x,y,z vectors) being a part of this 4-dimensional spacetime (in this case given by t,x,y,z 4-vectors), which is a chance for messing things in astronomy when one says "[[curvature of space]]" but means the "[[curvature of spacetime]]" (that is then called simply [[curvature of 4-space]]) that has to be flat in stationary universe though having its non zero '''curvatures of spacetime''' adding to the flatness of whole [[spacetime]].

[[Curvature of spacetime]] (singular as opposed to plural "curvatures") is something that describes a fact that some 4-dimensional space is curved. It can't happen though in a stationary universe since the [[spacetime]] of stationary universe has to be flat (or [[Minkowski]], which is another word for the same thing). In particular '''curvatures of spacetime''' may describe the curvature of the common 3-dimenssional space (given by x,y,z vectors) being a part of this 4-dimensional spacetime (in this case given by t,x,y,z 4-vectors), which is a chance for messing things in astronomy when one says "[[curvature of space]]" but means the "[[curvature of spacetime]]" (that is then called simply [[curvature of 4-space]]) that has to be flat in stationary universe though having its non zero '''curvatures of spacetime''' adding to the flatness of whole [[spacetime]].

The 4-space has to be flat in stationary universe since parallel transport of 4-vectors along geodesic lines can't change the angles of those vectors for the reason of conservation of energy and momentum: the 4-vectors have to come back after the parallel transport being directd in the same direction and with the same magnitudes  as before the transport by [[Noether theorem]]. To keep energy and momentum conserved there can't be any changes in components of those vectors.

The 4-space has to be flat in stationary universe since parallel transport of 4-vectors along geodesic lines can't change the angles of those vectors for the reason of conservation of energy and momentum: the 4-vectors have to come back after the parallel transport being directd in the same direction and with the same magnitudes  as before the transport by [[Noether theorem]]. To keep energy and momentum conserved there can't be any permanent changes in components of those vectors between ''"now"'' and ''"past"'' or ''"future"''.

   

   

That's why it is often important to be aware of various subtleties of names used in physics not to violate suddenly the conservation of energy and/or momentum by requring "gravity to happen in a [[curved spacetime]]", while it is not required by any physical or geometrical law.

That's why it is often important to be aware of various subtleties of names used in physics not to violate suddenly the conservation of energy and/or momentum by requring "gravity to happen in a [[curved spacetime]]", while it is not required by any physical or geometrical law.

[[Category: Physics]]

[[Category: Physics]]