Why are primordial black holes considered non-baryonic? A very important question that has been bugging me is why do people consider primordial black holes to be non-baryonic. I know that such a statement is then used to saying that they can be considered as dark matter candidates. I have also heard that stellar black holes are considered baryonic. Can anyone help me out understanding these concepts?
 A: I will just cite the introduction of a (relatively) recent paper by Carr et al.: arXiv:1607.06077

Since PBHs formed in the radiation-dominated era, they are not subjectto the well-known big bang nucleosynthesis (BBNS) constraint that baryons can have at most 5% of the critical density. They should therefore be classed as non-baryonic and from a dynamical perspective they behave like any other form of cold dark matter (CDM).

So the argument is just that. In part this is nomenclature out of book keeping convenience. In reality, some part of the mass-energy that contributed to the collapse of the primordial black holes may have come from baryonic particles. Alhthough, since they formed in radiation dominated era most of their mass should have come from non-baryonic mass-energy.
Stellar black holes on the other hand have formed from the gravitational collapse of stars, which consists (mostly) of baryonic matter formed during big bang nucleosynthesis. Thus, for book keeping reasons, they should be counted as belong to the 5% of the total "matter" density coming  big bang nucleosynthesis.
Note that over the last few years there has been a resurgence of the idea that primordial black holes could contribute a significant fraction of dark matter. The earlier conclusion that they couldn't was based on the unnecessarily restrictive assumption that all primordial black holes would have the same (approximate) mass (in jargon: their spectrum was assumed to be monochromatic). Moreover, on re-examination some of the observational bounds turned out to be less restrictive than previously thought.
A: We should start by making clear what cosmologists mean by baryonic matter because it isn't the same as what particle physicists mean by baryons.
The light elements hydrogen, helium and small amounts of lithium and beryllium were formed in a process called Big Bang nucleosynthesis (BBN), and it's the matter formed by BBN that is referred to as baryonic matter. BBN is (we think) a well understood process, and in particular the ratios of the light element concentrations depend on the total density of the electrons, protons and neutrons from which they formed. So by observing the current ratios of these elements we can infer the total density of the baryonic matter, and we get the 4% or so of the total density of the universe corresponding to regular (non-dark) matter.
Black holes have formed from this baryonic matter as the universe evolved, but this just redistributes the matter and doesn't change its overall density so we consider these black holes part of the baryonic matter and call them baryonic black holes.
The argument is that primordial black holes may have formed just after inflation ended and before Big Bang nucleosynthesis. This allows them to evade the constraints on the baryonic matter density imposed by the observed ratios of the elements in the universe. In this sense the primordial black holes are non-baryonic i.e. they would form part of the 27% of stuff in the universe that we call dark matter. However the primordial black holes would have been formed from electrons, protons and neutrons, and of course protons and neutrons are baryons.
But even the existence of primordial black holes is speculative, let alone their detailed properties. At our current state of knowledge to make claims about the nature of primordial black holes seems rather premature.
A: There are two dark matter problems.
Most of the gravitating matter in the universe is "dark" and cannot be detected by the radiation it emits, but its presence is deduced by studying the dynamics of galaxies and clusters of galaxies.
From analysis of the cosmic abundances of helium, deuterium and lithium, it can be inferred that most of the gravitating matter was not present in the form of free, interacting baryons in the first few minutes of the universe.
Thus the two problems are that most of the matter is "dark" and that most of this dark matter is "non-baryonic".
Primordial black holes could be a contributor to non-baryonic dark matter if they form (as is commonly supposed) before the epoch of primordial nucleosynthesis, since they would not then contribute to the baryon number density at that time. In fact, small primordial black holes likely form much earlier than this. The mass of a primordial black hole is expected to be proprtional to the mass within the particle horizon at time $t$, such that (e.g. Ackermann et al. 2018)
$$ M_{PBH} \sim 10^{12} \left(\frac{t}{10^{-23} {\rm s}}\right)\ {\rm kg}$$
Depending therefore on the exact epoch of "baryogenesis" and the value(s) of $M_{PBH}$, it is quite possible that primordial black holes may have formed before baryons existed at all.
Primordial black holes, because of their small size, could form an almost collisionless fluid that only interacted gravitationally with other bodies.
In other respects they are not similar to other non-baryonic dark matter candidates. Clearly, they could interact with light, in the sense that a black hole could absorb that light or bend it (other dark matter candidates could also interact gravitationally with light too). Notably though, they are also capable of emitting light in the form of Hawking radiation and the lack of any observed gamma ray "flashes" associated with the final moments of evaporating black holes or any enhanced gamma ray background,  suggests that dark matter is not made up of small $(<10^{15}$ kg) primordial black holes (e.g. Arbey et al. 2019).
