Black Holes in the Very Early Universe

[DrChinese]

The Schwarzschild Radius (R) is proportional to the mass M of the structure in question, and not its density. Let's suppose that the R(sun)=2 km for the sake of argument. And further let's suppose that if an amount of matter equal to our sun - M(sun) - is confined within a 2 km radius, it can never escape the confines of the black hole it is now within (by definition).

In the very early universe, say after .001 second, the main inflationary phase has ended. At this point the radius of the universe is on the order of perhaps 300+ km in radius. Every volume is much more dense than the sun. This doesn't matter, because the Schwarzschild radius of the entire universe is quite large and does not confine the hot expanding matter/energy of the young universe. Since the universe is expanding, but the total mass is essentially constant, density is dropping rapidly.

But at some point as the average denisty is dropping, subspaces containing matter equal to M(sun) approaches a size equal to R(sun). After all, today the average mass of a volume of space with a radius of 2 km is much much less than the M(sun).

So why didn't almost every bit of matter disappear into many black holes when this happened? I know that many black holes DID form during this period and these are now the centers of most galaxies. But it seems like almost every bit of matter should have ended up confined to one black hole or another, and therefore there would be little left of the universe for us to see today. Why isn't that the case? I would expect that we would live within a black hole of 2 km in size and seen nothing of the rest of our galaxy.

But we aren't. What happened?

 

[Physicsguru]

The Schwarzschild Radius (R) is proportional to the mass M of the structure in question, and not its density.

Would you mind proving this for me? Not that I cannot do it, but I want to look at some equations, to help me understand what you are trying to say.

Regards,

Guru

PS: Maybe you could start with a rapid derivation of the escape speed formula?

 

[Garth]

So why didn't almost every bit of matter disappear into many black holes when this happened? I know that many black holes DID form during this period and these are now the centers of most galaxies. But it seems like almost every bit of matter should have ended up confined to one black hole or another, and therefore there would be little left of the universe for us to see today. Why isn't that the case?

Perhaps it did.
In the “Freely Coasting” Cosmology the required helium abundance is obtained with a baryonic density of about 0.2 critical, in other words DM is baryonic afterall. However where is all this baryonic DM and why isn't it observed? One answer is the majority is in the form of massive black holes homogeneously distributed across the universe of say, 20% critical density, with 10% of that clumped into clusters - the Inter-cluster DM, and 10% of that in the form of visible stars. Total matter density 0.222 critical.

The standard LCDM model is not the only viable show in town!

Garth

 

[Chronos]

The universe did not collapse during infancy because it was expanding. The curvature of space-time is a function of mass density, but there is also a contribution due to expansion. The Schwarzschild solution is static. It only expresses the limit for a static spherical body before it collapses into a black hole. It does not apply to rapidly expanding matter. The other factor is the initial smoothness of matter distribution in the early universe. Matter was pulled equally in all directions until the extremely tiny local inhomogenities were sufficiently dispersed to become dominant. Local black holes could then form, but, the universe was much too large by this time and still expanding too rapidly to self collapse.

 

[Chronos]

Perhaps it did.
In the “Freely Coasting” Cosmology the required helium abindance is obtained with a baryonic density of about 0.2 critical, in other words DM is baryonic afterall. However where is all this baryonic DM and why isn't it observed? One answer is the majority is in the form of massive black holes homogeneously distributed across the universe of say, 20% critical density, with 10% of that clumped into clusters - the Inter-cluster DM, and 10% of that in the form of visible stars. Total matter density 0.222 critical.

The standard LCDM model is not the only viable show in town!

Garth

Massive ancient black holes? You mean like this one -
a black hole catalogued as SDSSp J1306 appears to be about one billion times as massive as the sun. It is 12.7 billion light-years away
http://www.cnn.com/2004/TECH/space/11/23/black.holeformation/index.html

Unfortunately, these denizens do not appear to exist in sufficient numbers to account for an appreciable amount of the missing dark matter:

A uniformly distributed population of supermassive black holes forming soon after the Big Bang do not, therefore, contribute significantly to the dark matter content of the Universe.
http://arxiv.org/abs/astro-ph/0101328
Prior studies have already ruled out abundances of SMBH larger than the 10E06 to 10E08 solar mass range addressed in this study.

 

[DrChinese]

The universe did not collapse during infancy because it was expanding. The curvature of space-time is a function of mass density, but there is also a contribution due to expansion. The Schwarzschild solution is static. It only expresses the limit for a static spherical body before it collapses into a black hole. It does not apply to rapidly expanding matter. The other factor is the initial smoothness of matter distribution in the early universe. Matter was pulled equally in all directions until the extremely tiny local inhomogenities were sufficiently dispersed to become dominant. Local black holes could then form, but, the universe was much too large by this time and still expanding too rapidly to self collapse.

OK, so if I understand correctly:

1. The Schwarzschild solution is for a static scenario, and the hot very early universe would not have formed black holes quite so early.

2. In my scenario, I don't think matter/energy homogeneity is an issue because what I am wanting to picture is how we got past some hypothetical phase transition in which nearly all matter disappears into black holes.

3. I realize that the inhomogeneity may have become very important a little later in forming the early primordial blacks holes that seem to populate the centers of most galaxies.

4. Presumably after T=300,000 years (or some value) the dynamic expansion component (as you describe) of most volumes of the universe fell to a point at which black holes could form if there were sufficient matter compressed inside its Schwarzschild radius. However, I am guessing that by the time this occurred that most of space was no longer dense enough for that to happen except in selected volumes of space due to inhogeneities.

Am I close?

 

[Chronos]

You got it. Let me just footnote item 2 from your post. Due to the extremely smooth matter density during the initial epoch, inflation occurs in flat [Minkowski] space. And due to expansion, the net curvature [gravity] is effectively negative during this era!

 

[Garth]

Massive ancient black holes?
Unfortunately, these denizens do not appear to exist in sufficient numbers to account for an appreciable amount of the missing dark matter:
http://arxiv.org/abs/astro-ph/0101328
Prior studies have already ruled out abundances of SMBH larger than the 10E06 to 10E08 solar mass range addressed in this study.

Thank you for that link, from the abstract:

This null result allows us to place a limit on the cosmological abundance of intergalactic supermassive compact objects in the mass range $\sim 10^{6}$ to $\sim 10^{8}$M$_{\odot}$; such objects cannot make up more than $\sim 1%$ of the closure density (95% confidence). A uniformly distributed population of supermassive black holes forming soon after the Big Bang do not, therefore, contribute significantly to the dark matter content of the Universe.

If one accounts for almost all of DM by primordial black holes then one would expect a mass distribution function of such objects, the least massive forming in the densest epoch, the more massive forming later on.

Only a small percentage, <1% closure density, would be in the above "supermassive compact object" mass range; these would then form galaxy nucleii around which primordial gas accreted. The rest would have a range of masses right down to micro-black holes. In a "hand-waving" scenario one could speculate that the majority of the mass ended up in the intermediate range 3 - 10⁴ M_Sun.

Garth

 

[Chronos]

Good point. I'm just being obdurate. Don't forget there is a lower limit on 'tiny' black holes as well [the gamma ray flux thing]. I like to take your model for a test drive here and there. It does good things, but still crashes against the curb. Of course so does the 'standard' model. I'm just trying to throw out ideas.

 

[DrChinese]

Good point. I'm just being obdurate. Don't forget there is a lower limit on 'tiny' black holes as well [the gamma ray flux thing]. I like to take your model for a test drive here and there. It does good things, but still crashes against the curb. Of course so does the 'standard' model. I'm just trying to throw out ideas.

LOL

Thanks for the answer to my question!