I still don't understand why a black holes needs an inside at all. If they are equivalent to their surface then why not dispense with having an interior and just be a surface?
Why isn't the surface smaller then? Probably something inside is pushing out? It's full? Also on the way to a black hole bodies clearly have insides. Do they somehow evaporate the moment a black hole forms?
Edit: My understanding is that all bodies are the size that they are because the inner/outer pressure equalizes, and this has many equilibriums based on the makeup of the body. Black holes are the ultimate degenerate last-stand where the make up is basically raw "information" which cannot be compressed any further while allowing said information to be recovered, which seems to be a fact of our universe. And it just so happens that the amount of information is proportional to the surface area of the black hole rather than its volume, which is probably a statement about how efficiently information can be compressed in our universe. One dimension is redundant?
"Pressure" as a concept doesn't apply to black holes. They are the size they are because of their mass. The bigger the mass, the larger area where their gravity is so great light can't escape. Scientists model black holes as only have a mass and a spin on the inside because that's all the external universe cares about. Information being inscribed on the exterior is an artifact of tike dilating as an object approaches a black hole, iirc.
> Why isn't the surface smaller then? Probably something inside is pushing out?
Hoberman spheres expand and contract via forces that act only along the structures that make up the surface, and this is a simple classical object. I don't see why a more exotic physical object like a black hole couldn't only have properties defined by its surface.
> Why isn't the surface smaller then? Probably something inside is pushing out?
The surface of space doesn't require something in a higher dimension pushing it out. That such an object may appear to have internal volume from our perspective doesn't need to be any more real than the apparent depth behind a mirror.
Agreed. Couldn’t black holes warp spacetime to the extent that there is no such place as “inside”? Time dilation is infinite at the event horizon, after all.
As you approach the event horizon, your frame of reference slows asymptotically to match that of the black hole while the universe around you fast-forwards toward heat death. I’d expect the hawking radiation coming out at you to blue shift the closer you got until it was so bright as to be indistinguishable from a white hole. You’d never cross the event horizon; you’d be disintegrated and blasted outward into the distant future as part of that hawking radiation.
The time dilation at the event horizon is infinite for an external observer. It appears that the person falling into the black hole slows down and never passes the event horizon. They redshift until you can't see them anymore.
For the unfortunate person falling into the black hole, there is nothing special about the event horizon. The spacetime they experience is rotated (with respect to the external observer) in such a way that their "future" points toward the black hole.
In a very real sense, for external observers there isn't really an interior of the black hole. That "inside" spacetime is warped so much that it exists more in "the future" than the present.
Professor Brian Cox also says that from a string theory perspective there isn't really an inside of a black hole, it's just missing spacetime. I tried to find a reference for this but I couldn't find one. Perhaps in his book about black holes.
I'm no physicist so happy to be corrected on any of the above!
> For the unfortunate person falling into the black hole, there is nothing special about the event horizon.
This is from a simplified model using black holes with infinite lifetime, which is non-physical. Almost all textbook Penrose diagrams use this invalid assumption and shouldn't be relied upon..
Fundamentally, external observers and infalling observers can't disagree on "what happens", just the timing of events. If external observers never see someone falling in, then they didn't fall in.
> Fundamentally, external observers and infalling observers can't disagree on "what happens", just the timing of events. If external observers never see someone falling in, then they didn't fall in.
This isn't true. As long as the two observers can't communicate with each other, they absolutely can have different results. To put it in simpler terms, the requirement of physics is that an experiment has a unique result according to some rule, but different experiments can have different results even if they break our intuitions.
So, if you measure the position of a particle falling towards a blackhole, you will see it disappear at the event horizon, and perhaps be radiated out later as Hawking radiation from that same event horizon. If you measure the position of the same particle while you yourself are passing through the event horizon, you will it will record no special interaction and see the particle moving completely normally. Since you can't perform both experiments at once, and you can't relay any data from one to the other, there is no contradiction.
This is just another case of a duality in physics, similar to how some experiments measure electrons as point-like particles completely localized to a certain place, and others measure them as waves spread out over a very large area.
If that were true, then black holes would appear as extremely bright balls of red-shifted radiation, as all particles whose trajectory ever moved towards the center of the black hole would still be visible. This is obviously not true, black holes appear as completely black objects that might have an extremely bright ring or halo of matter orbiting.
Sure, timing of the events, but infinity kind of breaks it - if external observers don't see someone falling in, then they didn't fall in yet, and if external observers see that falling in takes an infinite time (as in this case), then that is on some sense just a difference in the timing of events - however, from the observer perspective where that thing takes a finite time, they will also get to observe what happens afterwards.
Black holes don’t live forever. In principle, an external observer could watch you until the black hole evaporates. As mentioned above, if they never saw you fall in, then you never fell in. GR allows for disagreement on durations of events but not the events themselves.
Most that I know would say that it was disapointingly too big and too general to make specific predictions tied to this specific universe we occupy, although it had early promise.
Brian Cox didn't even make the wikipedia page so its difficult to claim he had any major role in perpertaring it as a large scale fraud.
Laughing at someone who says “hey an idea that isn’t falsifiable isn’t a good theory and certainly not something that any other ideas or theories should be constructed upon is I think more serious than not.
There's a theological doctrine called https://en.wikipedia.org/wiki/Eschatological_verification that claims that statements like "there's God" or "there's afterlife" are perfectly fine verifiable scientific statements, except that their verification come after death or Second Coming.
Your comment reminds me of it.
A surface implies an interior, otherwise it's a just a point. A surface is a boundary, by definition there is another side, something that is being partitioned.
I like to picture poking your finger into a loosely knit jumper so that the weave bunches up densely around the outside of a large hole. If you think of an ant walking around on the threads, it would realise that there's an area of increased density. It would also notice that there's a boundary it can't get past, but if you asked it what the topology of the threads are on the "other side" of the boundary it wouldn't be able to give you an answer.
In my mind that is what a black hole is, a spherical hole in the fabric of spacetime with matter bunched up around it in a very thin shell. That's why their area is proportional to their mass instead of their volume, because there is no volume.
The area of the Sun and the Earth and every other self-gravitating body in hydrostatic equilibrium is also proportional to the body's mass. Volumes are weird though: unlike area, relativistic volume can depend on the body's (and the spacetime's) history and composition rather than just the body's mass. In general the spatial volumes inside massive bodies in curved spacetime are larger than in Euclidean-Newtonian space.
The volume deviation is carried in the Ricci tensor
The highest-scoring answer at https://physics.stackexchange.com/posts/36411/revisions is a fairly reasonable attempt to calculate the volume deviation for nonspinning ~spherically symmetric bodies with the masses of the Earth (~ 10^2 km^3) and the Sun (~ 10^12 km^3), compared to the Euclidean-Newtonian volumes. Qualitatively, dropping these symmetries and the uniformity of the matter will tend to make the volume deviation larger.
> there is no volume
The volume deviation becomes enormous for compact (relativistic) objects, and for black holes one has to exercise care in even defining a volume, since naive choices of coordinates will show a divergence. Typically the choice of a 3-space inside the horizon has a time-dependency, and most choices of 3-space will tend to grow towards the future.
Christodoulou & Rovelli's (C&R) approach: https://arxiv.org/abs/1411.2854 ("it is large" for the largest volume bounded by a BH's area should win some sort of award for understatement). https://arxiv.org/abs/0801.1734 (reference [5] of the 2014 C&R paper) takes a slightly different path to the same conclusion.
YC Ong (several other references, and a number of related later papers) has a nice article at https://plus.maths.org/content/dont-judge-black-hole-its-are... The prize quote: "To give an idea of how large the interior of a black hole could become, this formula estimates that the volume for Sagittarius A, the supermassive black hole at the centre of our Milky Way Galaxy, can fit a million solar systems, despite its Schwarzschild radius being only about 10 times the Earth-Moon distance. (Sagittarius A is actually a rotating black hole, so its geometry is not really well-described by the Schwarzschild solution, but this subtlety does not change the result by much.)" And: " These examples show that, in addition to the surprising property that the largest spherically symmetric volume of a black hole grows with time, in general, the idea that volume of a black hole grows with the size of its surface area is wrong. In other words, by comparing two black holes from the outside, we cannot, in general, infer that the "smaller" black hole contains a lesser amount of volume. "
The area of a Schwarzschild horizon is straightforward to define, and unique for constant mass. (Procedurally you could count the number of unique tangent planes at r_{schwarzschild}, but there are other ways of arriving at the area).
If your sweater "weave" represents a set of orbits around the black hole and your ant free-fall along those rather than walk, you are getting close to a solution of the geodesic equations for a black hole. A free-falling ant will stick quite firmly to geodesic motion around a black hole. However, there are definitely plunging orbits that will take the orbiting-ant inside the horizon, and there is an innermost stable circular orbit (ISCO) that isn't solid like the yarn: a small perturbation of an orbiting-ant there will knock it into or away from the BH. But an un-knocked ant can circle forever.
The ISCO (3r_{schwarzschild} for a Schwarzschild black hole) is quite a lot of ant-lengths above the horizon of a BH (2r_{schwarzschild}). Spinning black holes have a narrower gap between the ISCO and the point of no return.
The point of no return for a spinning hole is just that: the ant can't backtrack, but will continue moving "forward" from there, and for a massive enough black hole it could do so for an hour or more before it feels the discomfort that precedes spaghettification. The "no drama" conjecture holds that the freely-falling ant won't even notice crossing the point of no return, although astrophysically it is likely to have noticed things falling inwards on different trajectores even above the point of no return (at ISCO around an astrophysical black hole the ant has a good chance of being knocked by something on an intersecting trajectory).
> fabric of spacetime
Misleading terminology. It's not a substance. Spacetime is nothing more than a collection of possible trajectories, and none of them needs to be realized. (Our universe has an enormous number of unrealized trajectories compared to ones on which real bodies move).
> bunched up in a very thin shell
The "thin shell" is just a set of points of no return, and for an astrophysical black hole where exactly each point is can be rather fuzzy since it depends on the outside universe which is filled with moving ants (and galaxies).
The interior contains a singularity, which may as well be the entirety of the interior. Maybe it has a "degenerate interior", which is very different than a region of space.
I'm not a topological expert, but I'm pretty sure you can have a surface without an interior. A unit sphere would be a good example of a surface without an interior.
