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?
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?
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.
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.
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.
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!
* generally considered a large scale fraud,
* perpetrated by (UK's Professor Brian) cox
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.
I am, of course, joking but she posts this sort of easy and empty clickbait.
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.
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.
I don't believe this is the case -- the particle just becomes ever more redshifted.
I don’t think that not being able to communicate your results makes it not scientific.
Falling "through" a hologram on the surface would be physically indistinguishable to the person falling from falling into a volume.
The former is the boundary, the latter is the interior + boundary. One of the great arbitrary naming conventions of math.
Space-time is not Euclidean geometry under GR.
We don’t know this. It has been as far as we’ve measured. But there are compelling reasons to at least consider discrete spacetime.
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 volume deviation is carried in the Ricci tensor
https://en.wikipedia.org/wiki/Ricci_curvature#Direct_geometr...
http://arxiv.org/pdf/gr-qc/0401099v1 (section 5.2)
https://math.ucr.edu/home/baez/gr/outline2.html (bullet point 9)
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).