Regarding the question of unification of the forces it is usually presented the following diagram:
So it seems the matter of whether the forces are unified or not relates to how high the energy is.
My question (which may not even make sense, since I'm getting started with all of this) is the following: in a black hole is it possible that the energy is high enough so that the forces are unified?
Are black holes a possible setting to analyze the question of unification of the fundamental forces?
Your question whether black holes can explore the grand unification energies is a good one. The answer is complicated, but the simplest version is no, for astrophysical black holes, except possibly for miniature black holes that were created during the Big Bang, and are now gone, unless they left a gravitational wave imprint. There's is another possibility, and that is that there are more large dimensions in the universe, more below. The other possibility is that we get more information on BH horizons and physics, see also below.
Grand Unification (GUT, T for theory) is where the 3 elementary forces, not including gravity, may be unified. That's the electromagnetic, weak and strong force. That unification happen at an energy level of about $10^14$ TEV, which is about a tenth of the Planck energy. The Planck energy is the highest energy we can conceive for a particle, and the smallest size, because below that size (and for higher energies) we don't know what space, time or energy means. Out understanding breaks down, as it is also the energy and sizes at which gravity also unifies with the other forces, and we just don't know yet what space or time would means on a quantum theory of gravity. [in case you are confused remember that as we increase energies we probe smaller and smaller sizes. The Planck size is the smallest we can conceive without a quantum theory of gravity]
See the wiki article on GUT at https://en.m.wikipedia.org/wiki/Grand_Unified_Theory
See the Planck mass, and those kinds of scales, at https://en.m.wikipedia.org/wiki/Planck_mass
See the wiki article about quantum gravity at https://en.m.wikipedia.org/wiki/Quantum_gravity
The LHC energies are on the order of 10-20 TEVs, and can find particles, as it found the Higgs boson, at energies about 10 times that. That's roughly the electroweak unification scale (170 TEV or so). To explore GUT it would have to work at energies about 12 or so orders of magnitude higher. That's not going to happen with any terrestrial accelerometer
For black holes (BHs) to have the energies needed for that many TEVs, if spacetime is 4 dimensional, they need to be very small, on the order of 0.1 mm. Unfortunately when they are so small they evaporate, in a quick explosion, in less than a second, so if they were formed in the Big Bang (called primordial BHs) they are not around now. It is possible, but not clear how likely, that they existed back then and emitted some gravitational radiation we could see now, or some other imprint. The latter would have to be able to be seen somehow in the cosmic microwave background as some kinds of unexpected density perturbations. Any gravitational radiation we'd need much larger interferometers than terrestrial ones to have the sensitivity to see. There may be some other imprints that would be expected that have not been seen.
If the universe had some large extra dimensions (string and branes theory have not ruled them out and do theorize the possibility) then BHs might be able to be produced at smaller energies, possibly at LHC energies. They don't seem to have been produced, but always possible at somewhat higher energies. There are still searches for larger dimensions with various effects and theoretical constructs, but nothing positive at this point.
Those energies are what happens inside the BHs, because as one is reaching the singularity the energy goes up until it approaches the Planck energy, and we just don't know if they stabilize or something else happens. We don't have the physics to know
Another way of exploring those scales, the GUT and quantum gravity Planck scales, is most likely from cosmological observations or gravitational wave observation for the time soon after the Big Bang. The theoretical underpinnings for what constitutes a possible quantum gravity theory is still unclear, and may involve string theory, and it's version where a correspondence has been found for gravity and quantum field theory in the holographic principle. But we just don't know. See the wiki article on the holographic principle at https://en.m.wikipedia.org/wiki/Holographic_principle
If we could ever go or see far enough inside the horizon of a BH, we'd likely be seeing some physics related to unification. But seeing inside a horizon is not possible according to general relativity. We need a theory of quantum gravity to understand what if anything happens inside horizons (for sure deep inside, but some effects might also have an effect on the horizon - there is some theorizing that the horizon carries the BH information that would otherwise be lost, in some form.....some possibility that no local effects inside the BH imprint the information on the horizon, in accordance also with the holographic principle). All of that is being researched theoretically, and it is hoped that as we see more gravitational radiation from BHs, or as we see some images of large horizons with greater fidelity, we'll see something that would help us understand better what may be happening in that realm of very strong gravity.
This is a very good question. Clearly as you approach the singularity the tidal force on a body increases. For quarks and gluons this means baryons are quickly turned into a quark-gluon plasma. Then for the the Schwarzschild metric the singularity is coincident with the $i^+$ region where Hawking radiation ends the black hole. Everything then reaches the Planck temperature where the vacuum is probably most unstable.
The Higgs field has the effect of restricting the number of symmetries of the low energy vacuum away from those of the Lagrangian. The term hidden symmetry or secret symmetry was used quite a bit in the early 1980s in my college to graduate school years. This is not as fashionable a term these days. Yet in many ways that is what happens. The black hole does something similar. Holography indicates that the field theoretic description on the bulk is a massively redundant description, say with gauge redundancies etc, of the field theoretic (CFT on AdS etc) description of the event horizon. There is then a huge surjective map from the bulk to the boundary or holographic screen, and these redundancies are ultimately due to a field description veiled by the horizon. This is then ultimately on what we call the singularity. The BH interior, or the timelike singularity of a dS/AdS spacetime the contains this huge hidden symmetry. It is the "master symmetry" of the universe. The black hole and the Higgs particle then do something remarkably similar. This is then a possible route to understanding what the master symmetry of the universe is.
