The formation of the elements is an interesting question in astrophysics. For the discussion of this post, it is important to distinguish the few lightest elements from all the heavier ones.
Big bang nucleosynthesis explains how the lightest elements have been formed in the early days (actually seconds) of the universe.
After 10 seconds of its life, the universe was containing some protons, neutrons and electrons, as well as a lot of photons that were dominating its entire energy budget. Not a single element was present, except hydrogen as a hydrogen nucleus is a proton.
[image credits: JPL @ NASA ]
After these 10 seconds, the temperature was however still large enough so that the lightest of all elements (deuterium, tritium, helium-3 and helium-4, beryllium-7 and lithium-7) could be produced by successive neutron captures and nuclear fusion processes.
In practice, we start from hydrogen that captures one neutron to produce deuterium. Then a second neutron capture leads to helium-3. Proton, deuterium and helium-3 fusions finally allow to produce the other nuclei above-mentioned.
However, the absence of any element with 5 and 8 nucleons (a nucleon generically denotes a proton or a neutron) makes it impossible to produce anything outside the above list. In order to explain the formation of the heavier elements, stars are necessary.
By burning light elements in the dense environment of a star core, nuclear fusion allows to produce the heavier guys. Helium nuclei are first fused into carbon and oxygen, and elements up to iron and nickel are then produced successively, one step at a time.
Producing anything heavier is more complicated as we need to rely again on neutron capture. And for this, we need a neutron-enriched environment that is not realized in stars. Supernovae and neutron star fusions are the new key player.
Black holes and accretion disks
In order to understand how black holes work, it is good to start with the fact that the universe is flat (this stems from data) and general relativity.
[image credits: Mysid (CC BY-SA 3.0)]
The image on the right is a good analogy of what is going on. The universe, seen as a sheet of rubber, is a flat surface on large scales.
At the level of smaller scales, like the one of planets, stars or galaxies, the content of the universe deforms its structure and bends spacetime.
In our analogy, any massive body can be seen as a marble deforming our sheet of rubber. Not all marbles are however equal, some being denser and some being more compact. Their properties impact the way in which they deform spacetime, so that the magnitude of the deformation is proportional to the density of the body.
[image credits: Ksshd (CC BY-SA 4.0)]
This is illustrated on the figure on the left. The sun is much less dense than a neutron star, and the latter is itself less dense than a black hole. Black holes are so compact that the deformation is actually infinite.
This shows why black holes attract and eat everything. Roughly speaking, anything that gets too close to a black hole (past the so-called event horizon) has no other choice than following the spacetime deformation straight into the center of the black hole.
[image credits: NASA/ESA (public domain)]
For this reason, it is not uncommon that black holes are surrounded by a structure called an accretion disk.
When matter gets close to the black hole (due to gravity), it follows a trajectory that consists in an inwards spiral. Gravitational and friction forces makes the temperature raising, so that a huge part of the available energy is automatically converted into electromagnetic radiation.
Take-home message: heavy element formation in black hole accretion disks
We now have enough information to answer the question about the creation of heavy elements in black hole accretion disks.
When matter gets absorbed by a black hole, it turns out that the accretion disk is mainly made of hydrogen (and to a smaller extent of other light elements). Therefore, if the density and the temperate are large enough, the very same nuclear fusion processes that gave rise to the formation of the heavy elements in the early moments of the universe could occur.
In other words, all elements ranging up to nickel could be produced. For anything heavier than nickel, it is a different story. The accretion disk is not a neutron-enriched environment, so that it is extremely rare to get them produced. The conditions for triggering the necessary neutron captures are not realized.
However, black hole accretion disks generally do not reach the density required to get nuclear fusion processes started, despite their important temperature. Accretion is indeed a usually slow process, regardless of the black hole size (see here for a master thesis on the topic). And dense accretion disks correspond to extremely fast accretion.
There are way around to temporarily get the right conditions, but the amount of heavy element subsequently produced stays tiny (less 0.01 percent of the observed amount of heavy elements).
To conclude, whilst heavy element production in black hole accretion disks is technically possible, it is so rare that it barely contributes to the entire heavy element production process in the universe.
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