In the Big Crunch Theory it says that gravity (curvature in space-time) will stop the universe's expansion and gravity will cause the universe to contract on itself. My question is if gravity is a curvature in space into which other objects fall into, how does that cause space to contract on itself?
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2$\begingroup$ You are almost there, since gravity (in GR) is interpreted as curvature of space-time, this works both ways. Mass-Energy can curve space-time and curved space-time delineates the form of movement and change objects will undergo $\endgroup$– Nikos M.Commented Jun 1, 2014 at 4:20
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$\begingroup$ This is a bit like black-holes are (assumed to be) created. They start with an inital collapse and this collapse curves the space-time more and the curvature causes more collapse $\endgroup$– Nikos M.Commented Jun 1, 2014 at 4:22
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3 Answers
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You've undoubtably seen the rubber sheet analogy for spacetime curvature, and I'd guess you're thinking that things fall into the dimples on the sheet. This is certainly true and is an analogy for how gravity works between astronomical bodies like stars.
However the rubber sheet as a whole can expand and contract, and this is an analogy for how spacetime as a whole expands and contracts. For a closed universe you have to imagine the rubber sheet expanding at early times as the universe expands, reaching a maximum stretch, then shrinking again at later times as the universe contracts.
The usual caveats apply: be cautious about taking the rubber sheet analogy too literally. Googling will find you many articles describing the deficiencies of the rubber sheet analogy e.g. this one. Also note that in the contraction phase we are not talking about a finite sheet contracting to a point. The sheet is infinite at all times - the contraction to a singularity means the spacing between any two randomly chosen points on the sheet goes to zero at the Big Crunch.
answered Jun 1, 2014 at 10:15
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$\begingroup$ Is gravity the cause of the space of the two points going to zero? $\endgroup$ Commented Jun 1, 2014 at 17:58
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1$\begingroup$ @user122083: the evolution of the universe is dictated by Einstein's equations of GR and the distribution of matter. The result is that we get a singularity at the Big Bang and if the universe collapses we get another singularity at the Big Crunch. $\endgroup$ Commented Jun 1, 2014 at 19:23
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In general relativity, as MIT Prof. Edmund Bertschinger said, matter tells spacetime how to curve, and spacetime tells matter how to move. If we have an energy-momentum tensor $T_{\mu\nu}$, the field equations,
$$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi G \, T_{\mu\nu}$$
dictate the geometry of spacetime by specifying the metric $g_{\mu\nu}$. If we have a matter source which gives rise to a metric $g_{\mu\nu}(t)$ which at some point in time $t$ means that spacetime becomes contracted, then that is what will happen, unless we change $T_{\mu\nu}$ by perturbing the system.
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think about spacetime as the higgs field with boson - boson bonds imagine a three dimensional space in a mesh format if you place a planet or black hole into a postion on this mesh its curves some curves stretch the fabric thus increasing the time it takes to travel via the curved path. some curves may also contract shortening the path so travelling through space on what appears to be a linear path to another galaxy say but that spacetime has been curved contractedly may shorten the distance to the destination thus time is contracted. the greater the gravity the slower time travels the lessor gravity the faster time travels. imagine a black hole with increasing gravity by bending and warping spacetime around it. as you travel toward it time slows down. now extend that concept by increasing mass to a critical point. mathematically there may exist a point where time stops completely stands still.