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Just to be sure, according to the theory of General Relativity, my understanding is that mass curves space-time. My question is, can mass also curve space?

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    $\begingroup$ Space is described in the space-like part of the metric, so I would think so. $\endgroup$ – HDE 226868 Apr 3 '15 at 17:59
  • $\begingroup$ yes, mass curves space-time, is space and time ;) $\endgroup$ – image Apr 3 '15 at 18:15
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    $\begingroup$ Though note that there are certainly cases where, while the whole spacetime is curved, there exist foliations where there are uncurved spatial sections, as in the flat robertson walker cosmology. $\endgroup$ – Jerry Schirmer Apr 3 '15 at 18:21
  • $\begingroup$ The question is not precise enough as there is no single way of breaking space-time into space and time. $\endgroup$ – MBN Apr 3 '15 at 19:36
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    $\begingroup$ @JerrySchirmer or conversely even when the whole spacetime is flat it can be foliated into curved spatial sections. E.g. the Milne metric describes a region of flat Minkowski space, but its spatial sections are curved. So it is entirely a question of foliation. $\endgroup$ – John Davis Apr 4 '15 at 2:54
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Yes. Space and time are both technically a single entity. The curvature of space-time is actually pretty famous.

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  • $\begingroup$ So a neutrino a billion light-years from us curves space that our Earth occupies? $\endgroup$ – Jiminion Apr 3 '15 at 19:55
  • $\begingroup$ Gravitational force approaches zero as the distance between approaches infinity. $\endgroup$ – Vatsal Manot Apr 3 '15 at 19:58
  • $\begingroup$ @VatsalManot I think that he is referring to the speed of a gravitational wave $\endgroup$ – Jimmy360 Apr 3 '15 at 20:04
  • $\begingroup$ No on both counts. I'm wondering if gravity can become so small it peters out and is 0. Alternatively, would it be so small as to be below the noise of the quantum foam and also be (effectively) 0. $\endgroup$ – Jiminion Apr 3 '15 at 20:24
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It's more sensible to talk about spacetime curvature than spatial curvature as the latter depends on how you foliate spacetime. For example de Sitter spacetime is not flat, but it can be foliated in ways that gives you flat spatial slices and in ways that give you curved spatial slices.

One way of seeing that gravity can never be described as purely spatial curvature is that whilst the path of a test particle in a gravitational field is independent of its mass, it is not independent of its speed.

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