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Comment by SpikeDad | Hacker News Reader

Confused because all of the stuff I've read and the videos from respected physicists say that there's no way the total mass of black holes could even be 5% of the predicted amount of dark matter that would have to be present to explain the motion of matter in the universe.

Of course this is way above my pay grade.

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I’ve heard the same claim, and the reason given was that microlensing surveys would have found more of these black holes. The article gets into this near the end:

> For example, perhaps the strongest constraints on primordial black holes come from microlensing searches [...] In these efforts, astronomers monitor bright but distant sources, waiting to see if a dark object passes in front of them. These searches have long ruled out an evenly dispersed population of small black holes.

> But if primordial black holes exist at a range of masses, and if they’re packed into dense, massive clusters, those results could be less significant than researchers thought, García-Bellido said.

I heard about this most recently on Sean Carroll’s podcast:

https://www.preposterousuniverse.com/podcast/2020/05/11/96-l...

The lack of microlensing evidence is one reason. The other is that there are constraints on the amount of baryonic matter in the universe from nucleosynthesis calculations in the Big Bang (i.e. the extra missing matter needed to account for galactic rotation curves can't be 'ordinary' matter).

https://ned.ipac.caltech.edu/level5/March10/Garrett/Garrett3...

Primordial black hole would have formed before big bang nucleosynthesis and so would not contribute to the relevant amount of baryonic matter.

> Primordial black hole would have formed before big bang nucleosynthesis and so would not contribute to the relevant amount of baryonic matter.

What would they have been made up? Do quarks have mass, and there was enough of them? Or does energy through E=MC^2 mean that enough pure energy density can cause a black hole?

> Or does energy through E=MC^2 mean that enough pure energy density can cause a black hole?

Yes! https://en.wikipedia.org/wiki/Kugelblitz_(astrophysics)

>What would they have been made up? Do quarks have mass, and there was enough of them? Or does energy through E=MC^2 mean that enough pure energy density can cause a black hole?

I'm not sure exactly when primordial blackholes would have formed but I think it would have been sometime after inflation, though perhaps before baryogenesis. Here's the reasoning: I think it would be after the GUT epoch so gravity would have splintered off from the other forces and I think it would have been after inflation started so that inflation had a chance to exaggerate the scale of quantum fluctuations to create the necessary size & scale of density fluctuations for blackholes to form.

Energy alone is enough to form a blackhole. However, it's not the energy density per se. That's sort of a necessary but not sufficient condition since you also need the surrounding spacetime to be at a low enough density relative to the region where you are expecting a blackhole to form.

This, incidentally is a common source of confusion about the big bang. "Why didn't it just form a blackhole?" The answer is because ALL of the spacetime was at the same density.

What does it mean for spacetime to have density?

I could say that a small sphere is denser than a large sphere because the distances between points are smaller on average, but that requires the spheres to be embedded in something with a distance metric(Euclidean 3-dimensional space).

What is the thing that spacetime is embedded in that provides a pointwise distance metric?

This can be (kinda) explained via the notion of space-time expansion. (This is an intrinsic phenomenon, having nothing to do with objects moving through space.) As the space-time expands, its density becomes lower. The (relative) change in density can be measured indirectly by measuring (the effects of) the expansion.

A technical explanation of the expansion involves the inflaton field.

(There's also energy density of the gravitational field.)

This may help: Given a spacetime manifold with metric and no matter that is flat an infinity, you can mathematically define the amount of curvature in it, which is directly related to how much energy in conventional forms (say, kinetic) that could be transferred to matter. Just as two merging black holes can emit gravitational waves, which have energy in this sense and escape to infinity, gravitational waves coming in from infinity can collapse into a black hole where no black hole previously existed.

Black holes are same as any other matter and the lensing is only dependent on mass. So if in a distant galaxy there is dark matter, the lensing will be exactly the same regardless fo whether this is in a form of cloud of particles or from billions of small black holes.

Microlensing surveys look for lensing of light from distant sources caused by relatively nearby masses.

The reasoning appears to be that if the BHs are clumped, then the number of microlensing events will be lowered, as opposed to if the BHs are evenly dispersed.

In other words, the number of concentrated masses intercepting rays of light from distant background sources would be given by the number of BH clusters as opposed to the number of BHs.

The objects we're looking for are large masses in the space between us and the distant light source. Typically the light source would be in the LMC or in our own galactic center, and the BHs would be, for example, in our own galactic halo.

We wouldn't expect to be finding BHs in a distant galaxy by microlensing.

I'm describing (or trying to describe!) what seems to be the astrophysics consensus. Sean Carroll is a Caltech astrophysicist who was interviewing another astrophysicist, and my quote from the article gives the explanation from a third. Am I getting this wrong?

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