One thing that changes how your clock flows is being in a gravity well. We have clocks which can measure it over just a few feet of height difference. Gravity isn't so much a "force" but the bending of space and time. Clocks moving differently is the result.

Same goes for people that stay on the moon, when they go back to earth their watches are slightly different than those on earth. GPS satellites need to be synced with earth clock periodically as well for this reason.

Now a detail that really makes things more interesting is that gravity is not constant upon the surface ( https://svs.gsfc.nasa.gov/11234 ), due to mass variations. So with that, it would be interesting to work out the age difference as a surface map. Though would need to historically adjust for tectonic shifts and other effects upon the surface mass. Of course the difference won't be as large, but still, I'd dare say that a day or so, would be more than viable upon the scale of things.

https://en.wikipedia.org/wiki/Time_dilation

> If you want an even more stark illustration of gravity’s effect on time, take the Sun - the team calculates that the Sun’s core is around 40,000 years younger than its surface.

Wow!

https://www.smithsonianmag.com/smithsonian-institution/ask-s...

Force is the derivative of this potential, so the abscence of forces in the center indicates an extremum.

If it were a hollow sphere with the same total mass as our actual Earth, as measured from the outside, then clocks everywhere inside the hollow sphere would run slow relative to clocks just on the outer surface of the sphere, by roughly the same amount as clocks at the center of the actual Earth. The "clock rate" in the interior of the sphere's material would decrease a lot faster, per unit distance down from the outer surface, than it does in our actual Earth, because the material of the hollow sphere would have to be a lot denser than the material of our actual Earth, in order to have the same total mass.

https://www.sciencealert.com/earth-s-core-is-2-5-years-young...

Equating being "a European nation" with EU membership is surely a trolling.

I am in awe of these words and fail to understand them in equal parts.

Assuming an exact black hole solution to the Einstein Field Equations (EFEs), what's happening is that any observer sufficiently close to the singularity will inevitably collide with the singularity. One can then define the horizon the outer boundary at which the future light cone attached at every point ends in the singularity. In order to avoid the singularity in the future one would need a causal cone broader than that of the light cone. The boundary is only a surface in the abstract; it's not material, you can't touch it, nothing bounces off it, and the no-drama conjecture says that if you were to float through the horizon you won't immediately notice you've done so.

Outside the horizon as defined above, some part of the future light cone will have the singularity in it, however as one choose an observer at a point further and further away from the black hole, the singularity occupies a smaller and smaller part of the future light cone for that observer at that point, and the observer would have to aim ever more carefully to collide with it. (The observer simply has to reach a point at the horizon).

> a black hole has nothing underneath the event horizon

That's true of vacuum solutions of the EFEs which contain black holes, but it's not true in general. The Vaiyda metric is an exact solution which equips a spherically symmetrical central mass with spherically symmetric non-interacting dust of incoming and/or outgoing radiation: a Vaiyda black hole can have some incoming radiation within the horizon.

Astrophysical black holes are more complicated since the matter outside them is generally far from spherically symmetrical. However, within the horizon will be some of the cosmic microwave background's (CMB's) photon gas, and whatever else reaches the horizon.

But, you're right that something must be deep inside an astrophysical black hole, and the something is perhaps not a classical singularity, but rather some configuration that preserves the quantum mechanical properties of the field-content that reached the horizon.

> might evolve over time

If there's infalling matter, it must evolve over time, as the mass will increase, and likely so will the angular momentum, and charges are likely to go back-and-forth as one cannot guarantee that only chargless matter (e.g. photons) will fall in, nor that if we let charged matter fall in, it will always be charge-neutralized (e.g., no ions allowed!). That's true of a classical singularity, and it will be even more true for any ultradense non-singularity structure that preserves QFT information.

> faster-than-light cascade of space-time

What's that?

> Gravity is affected by curvature

In General Relativity, gravity is curvature.

> whatever might be in the centre cannot be the cause of the event horizon

Mass-energy generates the metric. In the case of the Schwarzschild black hole solution to the EFEs, the central mass (which is all the mass and energy in the vacuum Schwarzschild spacetime) is static and concentrated at one point. However, a non-rotating star, or a slowly-rotating object like the moon, generates a very close approximation of the Schwarzschild solution. Astrophysical black holes generate an approximation of the vacuum Schwarzschild black hole spacetime, but the Kerr metric is a better approximation for rotating black holes, and there is plenty of matter in the universe outside black holes. The true metric of the entire universe is much much more complicated than our (useful!) approximations, but nevertheless it is determined by the scatter of mass-energy throughout the spacetime. The true metric almost certianly describes regions which behave almost indistinguishably from the interiors of Schwarzschild (and Kerr, etc.) black holes.

Another way of looking at this: as one throws matter into a black hole, the mass of the black hole increases, and so therefore does the diameter of the black hole. If you allow matter to cross into the black hole and collide with the singularity (or whatever replaces it), how can you maintain the italicized part of the quote above?

> the event horizon is stable in itself

If you allow mass to increase by letting dust and gas and cosmic microwaves reach the horizon, how do you keep the horizon stable?

Moreover, if you merge two black holes, how do you keep both black holes' horizons stable?

> It's a self-sustaining

Given Hawking radiation then a black hole that's a solution to the Einstien Field Equations and equipped with one or more quantum fields filling the whole spacetime where the energy-density of the quantum fields is below a critical threshold will shrink. In the limit of quantum vacuum outside, this shrinking becomes complete evaporation: the horizon simply is not found in the future, because the mass in the whole spacetime has reconfigured from concentration at a central point to diffusion away from the central point. Since mass-energy generates the metric, the metric ceases to be Schwarzschild (or whatever black hole metric had existed prior to final evaporation).

In our universe, there is lots of mass-energy outside black holes, and even though the metric expansion of space will make the CMB energy-density very small, it will still be higher than the critical threshold for stellar mass and larger black holes for a lonnnnnng time. But this isn't the black holes self-sustaining: they would evaporate, except for the CMB dust falling onto them, so it's the CMB (and its neutrino equivalent) that's doing the sustaining.

For starters, there are probably lots of black holes in our universe (and even in our galaxy). What happens if the unfortunate friend falling into the black hole is being watched from an orbit close to another black hole?

(General Relativity has the somewhat frustrating property that adding a black hole to a black hole spacetime does not obey the principle of linear superposition, so things can get quite messy if the two black holes in the paragraph above are close together. One can get even kinkier, for instance by considering a stellar-mass black hole orbiting a supermassive black hole, and kinkier still if both of them rotate with unaligned rotational axes and/or with opposite spins.)

Next, the metric expansion of space means that an isolated black hole would be more like a Schwarzschild-de Sitter solution. There we have the problem that two widely-separated observers can be highly cosmologically redshifted with respect to each other even if neither is anywhere near a black hole. One can of course also consider a collapsing universe in which two observers are blueshifted with respect to one another, and one could consider what that blueshift would do to observations by A of B if B were falling into a black hole in the collapsing universe.

Moreover, the presence of matter can make a mess of things. One can contrive an arrangement of matter near to a black hole which is sufficiently dense as to offset the gravitational time dilation of someone near the horizon.

Finally, there's kinematics: we can subject the unfortunate friend and the observer to a relative ultraboost wherein the doppler blueshift undoes the gravitational redshift.

A relatively ultraboosted Schwarzschild black hole would look a little odd to the relatively ultraboosted observer: https://en.wikipedia.org/wiki/Aichelburg%E2%80%93Sexl_ultrab... Things get weirder when you add other black holes, stars, dust, and so on to the Aichelburg-Sexl picture.

> From the outside, time does not appear to pass at all inside a black hole

From outside the event horizon of a static black hole there is no way to tell, even if one uses tricks like the above to do away with the objection that in general time appears to come to an effective standstill infinitesimally outside the horizon.

However, if the infaller brings in significant mass or angular momentum, we would expect the horizon to reflect the internal configuration change, since it's the internals that generate the horizon in the first place. This is a dynamical rather than a static (up to tiny perturbation) black hole.

This is extremely fiendishly difficult, and is run into in practice in terms of trying to work out exactly what the full theory says about the final merger of two black holes. Roughly speaking, the gravitational interactions between two merging black holes is best described by a metric wherein there is an effective third (and sometimes fourth) body.

Also not sure it makes sense for non-eternal BHs. For a BH that forms by gravitational collapse and eventually completely evaporates, surely the singularity has a timelike worldline? Some "lucky" too-early infallers (a cosmic neutrino, say) might pass through the centre collapsing progenitor before the horizon forms, while too-late infallers might pass through the region after final evaporation (assuming no horizon-equipped remnant). The "just-miss" is depends on where in spacetime the coincidence happens, and any reasonable slicing or threading would attribute the miss to being at the wrong moment in time.

Maybe easiest to think about that if the singularity is not always at the spatial origin of a system of coordinates. For instance, if SN1987a's remnant contains a black hole, that black hole is surely moving around the galaxy with the luminous matter "now", but before the final collapse there was neither horizon nor singularity.

I'm also perhaps unreasonably superstitious about the slogan's survival of arbitrary parameterizations, e.g., one can do an affine parameter on even an eternal BH's singularity and have what looks like a decent proper time for it.

Perhaps another way of putting it is that the usual Carter-Penrose BH diagrams showing long horizontal wavy line segments for the singularity are misleading because of exaggerations caused by the particular conformal chart it uses, kinda like how the Earth's very-near-polar regions are not that big even though they look that way on Mercator charts (those are also conformal, and you get really different results in the near-polar regions in other conformal projections even as closely related as a transverse Mercator/Gauss conformal projection, https://en.wikipedia.org/wiki/Map_projection#/media/File:Usg... versus https://commons.wikimedia.org/wiki/File:Usgs_map_traverse_me... ).

Just thinking aloud in the wee hours, and maybe having given too little weight (pardon the pun) to the qualification "inside the horizon" just before your close paren. There's a lot of rigour that can be hidden in those three words.