Exploring the Connection Between Empty Space and Einstein's 4D Space-Time

[delplace]

As you know 99.9999 % of our world is empty. Does this empty space correspond to Einstein 4D space-time.

 

[Nabeshin]

Well any well-behaved region of space, viewed close up enough, looks like 4D minkowski space. However, even though such a vast majority of space is devoid of matter, as a general rule space does not look flat on larger scales.

 

[delplace]

well, you point out my problem, how a void 4D space (according to GR) can be bent by few matter ? the only way I can understand it is in neutron stars because they are a "big neutron" without void. Does it mean in a rough approximation that universe curvature is due do neutron stars and black holes ?

 

[Dmitry67]

1. It is not important if space is empty or not. What is important is average density
2. The interesting property of GR is that if (in abstract static universe) you make a bigger and bigger ball of something, you eventually end with a black hole. So you can make a BH of water, air or even interstellar gas. So BH does not need to be 'dense'

 

[delplace]

Sorry but I don't agree
1. I would like to understand how something empty can be bent. Think 99.9999999% empty !
2. I know that BH formation need an enormous density and not only a big size !

Kindly :-)

 

[hamster143]

Sorry but I don't agree
1. I would like to understand how something empty can be bent. Think 99.9999999% empty !

It's also 0.000...001% bent.

 

[delplace]

yes :-)

 

[Dmitry67]

Sorry but I don't agree
1. I would like to understand how something empty can be bent. Think 99.9999999% empty !
2. I know that BH formation need an enormous density and not only a big size !

Kindly :-)

2. No
Only stellar size BH have high density
Check the formula for Scharshield radius:

http://en.wikipedia.org/wiki/Black_hole

r = 2GM/c^2

It is proportional to the mass! While when density is the same, mass is proportional to r^3

 

[delplace]

Your interpretation of Schwartzhield formula is wrong. This equation give the radius where a star of mass M will be dense enough to produce a black hole ! BH formation is only a question of density.

 

[Dmitry67]

absolutely wrong.

for a given density p the mass M in a sphere of radius r is

M = 4/3 * pi * p * r^3

S. radius for the given M is

r = 2GM/c^2

hence

r = 1/sqrt( 8/3*pi* p )

So if your material is not dense enough, you just need to take more material.

 

[Dmitry67]

in fact you don't need any formulas to understand that.
Take Earth for example, it has r=6300km and Rsh=0.5cm
Add more and more material to Earth.

when you double r, the total mass increases as r^3
For 'earth' of r=10*6300km Rsh=0.5cm*1000=5m

Sooner or later schwarshield raduis 'catches up' with an actual one.

The same is applicable to the whole Universe - in that case it becomes closed (unless it is expanding)

 

[delplace]

you forget a G in your last equation (not important). More important is the interpretation of S. formula. The physical meaning is : if you take a planet of mass M and volume V; you will obtain a BH if you decrease the volume until you reach a density M/V sufficiently high. The radius will be the S. radius. Of course you will obtain the same result by increasing M but it is not possible because you can not add more matter.

 

[clamtrox]

1. I would like to understand how something empty can be bent. Think 99.9999999% empty !

First of all, spacetime is not "bent", it is curved. Secondly, what exactly is your objection to spacetime being mostly empty? General relativity even allows empty spacetimes that are curved (for example Schwartzschild solution).

2. I know that BH formation need an enormous density and not only a big size !

This is simply not correct, and trivially so. It would be a good idea to accept it. If I take a large enough batch of interstellar dust, to an outside observer the cloud will look like a black hole, and all the dust will collapse to the center in finite proper time. For any given (assume constant) density $$\rho$$, an event horizon will form if the radius of the cloud is $$r \gtrsim M_p / \sqrt{\rho}$$.

 

[delplace]

GR equation is for me clear : space-time is "curved" by energy (tensor in the right hand of GR equation).

Hawking think we could obtain BH in the LHC. It is not in agreement with your proposal.

 

[Dmitry67]

you forget a G in your last equation (not important). More important is the interpretation of S. formula. The physical meaning is : if you take a planet of mass M and volume V; you will obtain a BH if you decrease the volume until you reach a density M/V sufficiently high. The radius will be the S. radius. Of course you will obtain the same result by increasing M but it is not possible because you can not add more matter.

For a given planet - yes, because we fix M.
But the BH formation is not caused by HIGH DENSITY - as I showed, you can create a BH from cotton wool

 

[delplace]

I don't think that even if you take a lot of cotton wool :-) but I respect your way of thinking

best regards

 

[clamtrox]

GR equation is for me clear : space-time is "curved" by energy (tensor in the right hand of GR equation).

... and what exactly makes you think an empty spacetime is not curved? As you may know, Einstein equation is a partial differential equation of the metric, and PDE's can certainly have nontrivial solutions even with no source term...

Hawking think we could obtain BH in the LHC. It is not in agreement with your proposal.

I am sure you don't mind explaining this claim in detail.

 

[delplace]

yes, PDE's can be solved with no source term. But Einstein introduce one Tij. And my physical approach let me think that you need Energy to obtain deformations and then movement. For me GR equation describe the non steady state evolution of univers.

I could explain in details ! :-)

 

[mikeph]

It can be curved in a region with no source term though. A universe filled with a single star is still curved throughout, so it shouldn't be troubling to think that one with billions has some curvature too.