The singularity is a prediction of GTR, but GTR breaks down there too. This is why black holes are so exciting in the context of new theories which are complementary to GTR!
It even preserves relative motion ! If A and B are both falling towards the event horizon, their relative movement doesn't change : by that I mean that if it was 2 moons, and someone launched a rocket from A towards B, it would take, say 10 hours to get to B. When both fall towards the black hole that time can still lengthen from the perspective of someone standing on A or B. It can shorten. It can stay the same. Depends on how it was changing before they started falling in.
So it could simply be that relativity stretches the space time near the event horizon enough for everything to fit in there, like that tent in Harry Potter. It looks weird from the outside, but if you're falling into the black hole it's the opposite: everything outside of that (very, very large) space near the event horizon is what looks weird. But if the black hole is big enough, it looks weird, but ... not very much.
The entirely weird thing is, you can choose initial conditions where all distances lengthen proportionally, in fact that's the more common scenario. So for all objects that are falling into the black hole, and objects not falling into it, all distances lengthen. Make the black hole big enough and the difference between things falling into it and things orbiting it or even moving away are very very small indeed.
And now you look at our universe, and that's exactly what you see. The value of the cosmological constant (ie. the universe is expanding, but ever slower and it will never actually stop expanding) can be explained by the assumption that we're falling into a very, very large black hole.
There is a TON of work done on BHs and the formulations to try to bend our knowledge of QM and 'classical' physics to them. If you really want to get into the nitty gritty of it start with this [1]. It's a HARD road, but the proofs and knowledge in the field is mindblowingly cool. Go for it!
[0]https://en.wikipedia.org/wiki/Relativistic_electromagnetism
[1]https://www.amazon.com/Classical-Electrodynamics-Third-David...
I've still got my copy of Jackson from grad school. ;-)
You'll probably find MTW a lot more approachable after working through a few less beastly texts.
That's exactly the right number to describe the macroscopic state of a no-hair black hole (defined as the horizon as seen from the outside) using a set of spatial coordinates: mass, charge, angular momentum for three spacelike axes, linear momentum for three spacelike axes, and centre-of-mass position for three spacelike points. Here I have already done a foliation of spacetime into a spatial slice with a constant timelike coordinate; it'd be normal to use coordinates in which the centre of mass is always at the origin, which fixes the last six components at zero.
On the other hand, if we omit the spacetime foliation, we are obliged to use tensor quantities for these variables; moreover, if the spacetime region we consider is not "sufficiently small", then no-hair looks much more conjectural. Foliating this region, we would expect at least the charge no-hair number not to change from one slice to another. For a black hole with a highly ionized accretion disk with nuclei or electrons liable to cross the event horizon at any time, this is a tough ask (and the subject of research in numerical relativity).
> charm and strangeness
The larger the black hole, the flatter the spacetime just outside the event horizon; astrophysical black holes' immediate neighbourhood is too flat to break quark confinement, so a surplus of colour charge seems unlikely. Conversely, a black hole small enough that tidal effects are very strong just outside the horizon is likely to be evaporating so violently that gravitational effects on hadrons just outside the horizon seems (to me, anyway) less interesting than scattering interactions.
> What's the total number of numbers that accompany a particle as it gets sucked in?
Good question. This is an area of research.
Any answer raises a second question: how does "balding" work?
Even fully classically we have this problem: if we drop a thin uniform spherical shell of neutral matter of mass M into a Schwarzschild black hole (so there's no rotation or charge or quantum-anything to consider) how do we distinguish that black hole from an identical setup except we drop in two concentric shells of 1/2 M each?
If in some future region of spacetime when the shells are inside the BH (black hole) we can distinguish between BH with one shell vs BH with two shells, then no-hair is wrong. If we cannot distinguish, then classical information is lost.
This is black hole thermodynamics because we have a relationship between macrostates (the no-hair values) and microstates (the set of values that migrated from outside the BH to inside the BH), and we can define entropy in a Boltzmannian way using that relationship. If no-hair is accurate such that we can throw in an huge number of shells each with a tiny fraction of the mass of our single-shell example, then that black hole's entropy is enormous.
The quantum picture is in some ways "just" a complication of this fully classical information loss problem. If we can throw in whole molecules / bits-of-dust, atoms and ions of various masses, free electrons, photons, neutrinos, and so forth and still see a "no-hair" set of macroscopic variables, then a reasonable-size BH's entropy is enormous, and it gets much more enormous if we only increase the BH mass while keeping the other no-hair values always zero (and letting the others vary does not help much).
If in our universe we find a black hole which we can comfortably describe with a tiny number of variables (e.g. a no-hair black hole), we should expect that it will have lots of hidden microstates thanks to things having infallen (and indeed, for astrophysical black holes, lots of particles from the stellar remnant). Did these bald away in the past? Or, if black holes evaporate, will these hidden microstates be revealed during that process?
> what's inside
Good question. There's a wide variety of guesses by theoreticians.
As we increase our number of observations of BH-BH, BH-NS, and NS-NS (NS for neutron star) mergers where we get decent gravitational wave signals, we can exclude many possible answers to these problems.
Finally,
> an upper limit on the information content of a black hole
No-hair black holes' event horizons are determined by the no-hair variables alone; their entropy limit is related to the surface area of the horizon.
> a "civilization" inside it
We don't know without a full answer to "what's inside". The "Eldar" idea is that for an extremely massive black hole with an improbably large charge (how does one prevent such an object from drawing in matter of the opposite charge?) there may be stable orbits in an interior region. I think even that is a really big stretch.
But the stuff that falls in is not purely described by its mass. It also has angular momentum, electrical charge, maybe a few other quantities such as charm and strangeness (speculating here). So the black hole must have a net angular momentum, electrical charge, charm, and strangeness. Electrical charge could be measured by holding an electrometer next to the black hole. And so forth.
So far I've described 5 quantities that "describe" a black hole. So my question is: How many more are there? What's the total number of numbers that accompany a particle as it gets sucked in?
Suppose it's a small number, like 11. Does that place an upper limit on the information content of a black hole, and hence the possibility of describing a "civilization" inside it?