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[[Curvature of spacetime]] is something that describes a fact that some 4-dimensional space is curved which in our world is a myth when applied to our universe since its [[spacetime]] is flat (or [[Minkowski]], which is another word for the same thing). In particular it may describe also 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 cosmology when one says "[[curvature of space]]" but means the "[[curvature of spacetime]]" (that is then called simply [[curvature of 4-space]]). It happens a lot in cosmology when astronomers customarily mix [[curvature of space]] (the obvious feature of 3-space) with [[curvature of spacetime]] that has to be flat (otherwise known as [[Minkowski]]), though having its non zero '''curvatures of spacetime''' adding to the flatness of whole [[spacetime]].

[[Curvature of spacetime]] is something that describes a fact that some 4-dimensional space is curved which in our world is a myth when applied to our universe since its [[spacetime]] is flat (or [[Minkowski]], which is another word for the same thing). In particular it may describe also 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 cosmology when one says "[[curvature of space]]" but means the "[[curvature of spacetime]]" (that is then called simply [[curvature of 4-space]]). It happens a lot in cosmology when astronomers customarily mix [[curvature of space]] (the obvious feature of 3-space) with [[curvature of spacetime]] that has to be flat (otherwise known as [[Minkowski]]), though having its non zero '''curvatures of spacetime''' adding to the flatness of whole [[spacetime]].

The 4-space has to be flat since parallel transport of 4-vectors along its geodesic lines can't change the angles of those vectors for the reason of conservation of energy (the 4-vectors have to come back after the transport being directd in the same direction as before the transport since some of their components as energy or momentum in various directions must be conserved (by [[Loether theorem]]).

The 4-space has to be flat since parallel transport of 4-vectors along its geodesic lines can't change the angles of those vectors for the reason of conservation of energy (the 4-vectors have to come back after the transport being directd in the same direction as before the transport since some of their components as energy or momentum in various directions must be conserved (by [[Loether theorem]]).

   

   

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, since so far the nature does not know how to make energy or momentum from nothing.

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, since so far the nature does not know how to make energy or momentum from nothing.