# When the mass fills all of space in almost uniform density, can it sustain its state?

When the mass (wood, hardened sand, iced water, stone or whatever but is not so fluid) fills all of space (especially in a volume of infinite size) in almost uniform density, could the mass sustain its state/structure?

I'm afraid about that it will collapse into a planet or something. I think it could create a gravity equilibrium (?) state, but with my limited understanding of physics I cannot be sure of this situation.

• Welcome to WorldBuilding! If you have a moment please take the tour and visit the help center to learn more about the site. I am sorry, but I have no idea what you are asking. There seems to be a little language barrier or maybe it's just my understanding of physics that's at a loss here. What do you mean with "every space"? Are you asking about space in an astronomical sense? How is wood supposed to fill everything? Or are you asking about a large amount of wood/sand/... in space and whether it would form a planet, like in A Mole of Moles? – Secespitus Aug 10 '17 at 7:53
• Hello, QuietJoon, I have edited your question to make it easier for English speakers to read. Essentially your question is about an infinite space filled with solid matter of uniform density and whenever this will be stable. Enjoy yourself here. – a4android Aug 10 '17 at 8:32
• Hi, the exact answer to this is possibly going to depend on things like the topology of the space - is e.g. your universe spherical or toroidal? There's a chance that it won't make a difference, but my first guess is that it might – Mithrandir24601 Aug 10 '17 at 10:31
• Hi QuietJoon. I see you accepted an answer only 40 minutes after posting the question, and only 20 minutes after that answer was posted. While it is up to you when, which, and whether to accept an answer at all, it is generally recommended to wait at least a full day before accepting. Having accepted an answer indicates to the community that you feel your question has been satisfactorily answered, which can discourage others from providing alternative, possibly better, answers. Waiting a day allows people in different time zones to see your question and possibly post alternative answers. – a CVn Aug 10 '17 at 11:01
• How is this different from the Heat Death of the Universe? or is that not a thing any more? – Ralph Crown Aug 10 '17 at 20:17

In perfectly uniform density over an infinite volume, yes, but this equilibrium is unstable.

Any given point in an infinite volume of perfect uniformity is under no stress, effectively in the centre of an infinite shell. You have chosen a hard substance, rather than a gas which would be simpler, but the result is the same. The difference is that it's able to maintain a greater deviation from the perfect uniformity before the system breaks down.

As soon as there's an edge or a distortion, anything that breaks that perfect uniformity to an extent greater than the structural strength of your material, then the equilibrium breaks down and the mass will start to bead up (form planets or, because this is a high density substance, form black holes).

## No

The formula for a black holes radius is $2\frac{GM}{c^2}$

Radius grows with mass but volume grows with cube of radius. So if you pick a sufficiently large sphere in your infinite substance then it will be more massive than a blackhole of the same size. (Roughly how big?)

$\frac{2G}{c^2}=10^{-27}$

so

$M=10^{27}*r=10^3*r^3*\frac{4}{3}*\pi$ (assuming the density of water)

so

$10^{24}=r^2*\frac{4}{3}*\pi \approx r^2*4$

so

$r=\sqrt{\frac{10^{24}}{4}}=\frac{10^{12}}{2}=5*10^{11}$

so the material collapses into a black hole at a size of $5*10^{11}$ meters. For comparison the Earth is about $10^{11}$ meters from the sun.

(The reason this doesn't apply to the universe depends on the fact that the universe isn't very dense, has a finite (observable) size and is expanding.)

• I edited your answer to use Mathjax so that the formulas are easier to read. Could you please check if the math is still correct? – Secespitus Aug 10 '17 at 9:23
• It doesn't collapse because there's an equal force pulling out as in. Any given point is in perfect equilibrium as though inside an infinite shell. What this means is that you can't define an arbitrary sphere the way you have, you need a break to create an instability at which point yes, it will collapse into black holes, but while it remains an infinite perfectly uniform solid, it can't collapse. – Separatrix Aug 10 '17 at 9:26
• I feel your calculation is wrong. There is no wood or metal or whatever material with density equal to black hole, except black hole itself. – L.Dutch Aug 10 '17 at 9:53
• Isn't there an infinite force pulling things apart? – Innovine Aug 10 '17 at 12:54
• @Separatrix is correct. The derivation for Schwarzschild radius assumes that there is negligible gravity coming in from outside the Schwarzschild radius. – BobTheAverage Aug 10 '17 at 16:16