Are black holes exploding just like the singularity at the big bang did, we just can't see it because of time dilation? There is only a few question about exploding black holes but that does not address my question.
Can a black hole explode?
Is there a relationship between Black Holes and the Big Bang?
Did the Big Bang happen at a point?
Just to clarify, I do understand that:

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*the big band did not happen at a point


*the universe isn't expanding into anything
Now today we theoretically hypothesize that all black holes must contain a singularity, and this might show similarities (both are spacelike) with the singularity before the big bang.

Extrapolation of the expansion of the universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past.[18] This irregular behavior, known as the gravitational singularity

https://en.wikipedia.org/wiki/Big_Bang
So as far as I understand, inside black holes, there is extreme gravity, and extreme relative time dilation, so to us, outside observers, black holes seem to be relatively stationary objects. To be more precise, there might be some activities outside the event horizon, but the black hole (the region inside the event horizon) must appear relatively stationary. But to my understanding, we only see this appearance because of extreme time dilation. But do we know how black holes would evolve on the larger time scale, like are they expanding or exploding objects?
My question would be then, do we know how these black holes evolve on the larger timescale, do the singularities inside the black holes explode like the big bang?
Question:

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*Are black holes exploding just like the singularity at the big bang did, we just can't see it because of time dilation?

 A: No, black holes in General Relativity are not slowly exploding. However, you are correct that there is on analogy that can be drawn between cosmology and spherical collapse. You see, in classical relativistic cosmology there is not only the possibility of a Big Bang, but also of a Big Crunch. The Big Crunch is like the Big Bang just in reverse: Matter starts off at finite densities and then, by evolving a finite time into the future direction, you get an infinite blow-up in densities and a space-like curvature singularity in the entirety of space (as measured in the comoving cosmological frame).
Now the spherically symmetric collapse of a ball of matter looks quite similar in the frame comoving with the fluid. That is, you define your coordinate grid by attaching it to specks of matter comoving with the fluid. First, you see finite densities, and then suddenly, in a finite time in the future, there is an infinite blow-up and a space-like curvature singularity everywhere in the grid comoving with the fluid. So the fluid has experienced something like the Big Crunch, but maybe it was not as big, so let us call it a Small Crunch.
There is one thing that you got right as well, the infinite time-dilation sort of freezes this small crunch in. This means that if you want, you can approach the black hole and experience the small crunch as well, if you want. Just approach the horizon, dive in, and in a finite time you will have the pleasure of partaking in this cosmic event as well.

Since GR and all physics involved in the collapse are reversible, there is a version of this process that runs back in time. Physically, you would probably call it a white hole dispersion. Locally, in a frame comoving with the matter, the matter would start of in a curvature singularity of the sort of a Big Bang, but the amount of matter would be finite. So I guess we should call it a Small Bang. After that it would emerge from a repelling white-hole horizon (impossible to enter on a future-directed time-like curve). From the outside this would look like a white hole that was always there. And then suddenly it spits out all this matter (probably in a spectacular explosion) and then just disappers, there is no repelling horizon anymore. But remember, this is exactly the time-inverse of the black-hole collapse.
A: The black hole itself would not be exploding, but it might contain an event similar (but not identical) to an explosion, that would function locally as a big bang.
These processes are described in Nikodem Poplawski's torsion-based model, elaborated in numerous papers written between 2010 and 2020, whose preprints are available free on Cornell University's "Arxiv" website, at https://arxiv.org/a/poplawski_n_1.html .
His model's based on Einstein-Cartan Theory, worked out through conversations between Einstein and the mathematician Elie Cartan that occurred after the discovery of particulate spin, and were completed in 1929. Avoiding that idealization of fermions as "pointlike" which facilitates their analysis within our own inertial frame, it differs from 1915's General Relativity by allowing for fermions to have a tiny spatial extent, which remains greater than the Planck length.
In Poplawski's model, a large rotating star, whose exhaustion of its nuclear fuel has left it without radiation pressure adequate to resist its gravitational collapse, forms a black hole, whose event horizon propagates outward from its center, with tidal effects separating the particles of virtual pairs by the Compton wavelength for more than the Compton time, thereby materializing them from the gravitational potential.
Upon contact with the stellar fermions (which would be vastly larger), the inward trajectories of many of the newly-materialized particles are reversed and greatly accelerated outward, forming a new "local universe" whose shape Poplawski has compared to the skin of a basketball. (Through Feynman's interpretation of Maupertuis' Principle of Stationary Action, from which General Relativity can reportedly be derived, such particulate interactions can be generalized in terms of spatial expansion.) After its formation, the new LU would continue expanding inertially for an indefinitely long time, but would, nevertheless, remain causally-separated from the larger LU that had contained its "parenting" star.
The initial expansion of that LU would be asymptotically exponential, so the local universes formed through Poplawski's model would be formed by a version of cosmic inflation, without any need either for the hypothetical "inflaton" particle that would be needed in those earlier versions of inflation that depend upon a field of them, or for that singularity of infinite density which characterizes the original "Big Bang" models.
Because each of the LU's would, itself, eventually contain rotating stars apt to collapse gravitationally, ad infinitum, his model may, in the resolution of disparities between that "block universe" view of time which characterizes Einstein's relativity and the quantum physics relation of time to phenomena emerging from quantum entanglement, also contain some potential for resolving the fact that "vacuum energy" is hypothesized to have a value exponentially larger than that value which can be verified by observation.
As our own local universe would've originated within one or another of the black holes in a "parenting" LU, there would be some preferred direction of motion corresponding to the direction of rotation of the axis of whichever of that LU's stars had collapsed to form our own LU, leaving some possibility for that observational verification required of scientific hypotheses.  Results of the attempts at such verification that have been obtained to date remain inconclusive.
Regarding the part of the OP's question concerning the possible visibility of the quasi-explosive "bounce" to observers in the larger and older "parenting" LU outside the black hole, its larger scale and its own continuing expansion would suffice to keep the particulate interactions of that bounce permanently invisible to them, given the fact that the inertial frame of all objects remaining in the parenting LU would differ greatly from that of any of the objects involved in the bounce itself.
The "black hole information paradox" would be resolved by the transfer of information (i.e., heat) inward between "parenting" and "offspring" universes, rather than through the faint (and perhaps unverifiable) outward radiation hypothesized by Hawking.  The transmitted information might, once deciphered by civilizations sufficiently advanced, even result in artifice aimed at an intermittent self-perpetuation on sequentially-decreasing scales, by such means as the addition of mass to stars about to collapse into neutron stars, which could provoke their collapse into black holes instead.
The compatibility of Poplawski's model with the Cosmic Microwave Background radiation was detailed in a 2015 paper by Desai, titled "Non-parametric reconstruction of an inflaton potential" and freely available at https://arxiv.org/abs/1510.08834  .
In that "block universe" view of time which characterizes Einsteinian relativity, the actual point at which magnification energy otherwise adequate to reveal whatever internal details a local universe might (or might not) have would (through mass/energy equivalence) also cause its collapse into a hole blacker than that point's surface:  So, the unique objects chosen for representation only by a point might mark the limits of knowledge, but not of extant reality. The interesting thing is that the same curiosity motivating the assembly of any such magnification equipment would have also "illuminated" (if only by an absence of reflection) whatever intermediate black holes (each surrounding an LU) would've lain between the civilization assembling it and the object of its curiosity, which, if such illuminations would reveal a pattern, might open the possibility of a multiverse pulling itself into existence by its own bootstraps, and those of its occupants.  As has been pointed out by the late John Barrow of Cambridge, miniaturization would provide one route to survival during an approach to thermal equilibrium that might be kept asymptotic.
I've been interested in Poplawski's model mainly because of a nearly life-long interest in Olbers' Paradox, which its "Black Hole Genesis" resolves very simply.  Although that model's reliance on ECT may appear threatening to many physicists who have invested much time obtaining a really admirable mastery of General Relativity (Einstein-Cartan Theory's older forebear), Black Hole Genesis also provides the plainest answer to the OP's question about the lack of visible quasi-explosive effects in the context of a multiverse, and has versions based only on 1915's GR, as discussed by Brandenberger at  https://arxiv.org/pdf/hep-th/0103019.pdf, and in his paper's references.
