I'd recommend the two episodes released right before the one about the black hole information paradox too. They set up for what is covered in the information paradox episode.
Maybe the episode before those two also. I vaguely recall that something from the information paradox episode used something from that (and if I'm misremembering, it was still a neat episode):
I have a question about the episodes you cited. They cover how beyond the event horizon space becomes time and time becomes space. They go over how that means that inside you can't go backwards in space for the same reason that out here in the normal universe you can't go backwards in time. You are doomed to only go forward, which inside means toward the singularity.
(Much better than the ridiculous analogy often given that you can't get out of a black hole because the escape velocity equals or exceeds the speed of light. That's a ridiculous analogy because it only explains why you can't get out ballistically).
But all their explanations used a simplified black hole in a spacetime with just 1 space dimension and 1 time dimension. We've actually got 3 space dimension. Does that mean that in a real block hole past the event horizon, you end up in a spacetime with 3 time dimensions and 1 space dimension?
If so, does anything interesting happen due to having more than one time dimension?
From the perspective of an outside observer, nothing ever reaches past the event horizon- it just asymptotically approaches it. The same goes for the whole mass of the black of hole- from an outside perspective, it's smeared across the surface.
There isn't an object that messes with the warping of spacetime- the black hole IS the warp in spacetime. If changes in spacetime couldn't propagate away from the black hole, it wouldn't exist.
I understand that from an external POV things that fall into a black hole never seem to reach the event horizon, but there must be material that is inside the event horizon. When the original star collapsed and the black hole formed, there was material inside the volume enveloped by the new event horizon. Also as more matter accumulates in the accretion disc of the black hole the event horizon will expand. With these enormous super-massive black holes, with event horizons the size of earth's orbit, there must be something inside the event horizon.
Or is that wrong, and everything just smears out even more finely as the event horizon grows?
That one, anyway, is easy. Sort of. Gravity is our perception of space itself being stretched, squeezed, even twisted. So, no gravity is escaping; instead, the black hole is warping the space it is in.
The mathematics describing this process are intractable except in very special cases. In most cases, physicists are obliged to use an approximation that produces an answer that they hope has much of the character of the correct answer. At one extreme, they just use Newtonian gravity, which produces almost-exactly correct answers for small-scale systems involving just regular stars and planets. It is only when warpage gets very large compared to the size of the system, or when e.g. galaxy-scale mass is involved, or the differences between Newtonian gravity and reality are what is interesting, that they have to resort to more complicated approximations.
It was recently discovered that calculations of the motion of galaxies were using an insufficiently accurate approximation that made it seem like stuff is orbiting too fast for the visible mass, requiring "dark matter"–extra, invisible mass–to hold the galaxy together. But using a more accurate approximation makes the need for dark matter evaporate. This created a problem because astrophysicists and cosmologists have come up with lots more uses for dark matter, to explain lots of other things. Without dark matter, they have dug themselves into a hole. The response has generally been to ignore the more accurate galactic gravitational model, and double down on dark matter. They can do this because ultimately it is all just a matter of papers being published and careers advanced or blighted; there are no other real-world consequences.
This is not correct - electric charge can also escape from a black hole.
The actual answer is that it is energy that can not escape and a static gravitational field (or electromagnetic field) is not energy (in and of itself).
However keep in mind that time is frozen by a black hole, so if you have a black hole with a certain charge, and a new charge falls in, the "change" in charge never escapes (it takes infinite time to escape) so you have no issue of non-static gravity or charge escaping from a black hole.
Like the scrunching comment says about the shape. Light travels in straight lines. It just happens that all the straight lines from inside a black hole curve back in on itself. So the light travels as far as it wants but only within the confines of this curved spacetime.
There are a handful of replies already and I'm not any sort of authority on this subject. But, I'd like to share a few of the things about this that have made sense to me; maybe someone will add to or correct one of them and I'll learn something more.
Black holes and gravity are hard to get a satisfactory grasp on for laymen (like me) because they behave in ways that are unlike anything else in the natural, observable world around us. People try to understand difficult concepts by relating them to familiar things, but gravity and black holes don't relate to anything we're familiar with.
Gravity for example isn't, we think, a "thing". It's a property, or a consequence. [1] Lots of people are looking for some way to relate it to the physics of particles and electromagnetic forces, but that hasn't happened yet. So, gravity doesn't escape, or travel, because it isn't a "thing". There's no particle of gravity. There is a force, in that when we observe large masses, they seem to be acted upon by some kind of invisible action, but that force is actually a consequence of things attempting to travel in straight lines along a curved surface.
Changes in gravity do travel, apparently at the speed of light. So, in that sense, the gravitational effect of a black hole does extend beyond its event horizon. But, that's totally okay, because gravity itself isn't a thing and doesn't travel and therefore doesn't need to escape a black hole.
Rather, a black hole is a consequence of gravity, or relativity. It's a division-by-zero [2] in the equations that describe matter, gravity, and curved spacetime. Thinking of black holes as being somehow similar to really really dense planets is one of the misconceptions that misled me for a long time. They are instead more of a place where physics, as we understand it so far, stops working.
That place has a boundary region where physics still mostly works, and things happen there that we can sort of understand and relate to. We can observe some of the effects of this extreme curvature of spacetime in this boundary region.
But beyond that, the curvature goes to infinity and volume goes to 0 and time stops existing.
There's an old joke about black holes being where god divided by zero. Since god can do all things, dividing by zero is not impossible. Once we can comprehend how dividing by zero is possible, the mysteries of black holes will be revealed.
As best as I understand: light travels in space. Thus, if space is scrunched up, light can't escape. Gravity IS space. The scrunching up IS gravity. There is no "escaping", because gravity is literally the substrate.
For most 3+1 dimensional theories containing gravitons they do so in exactly the same way classical gravitational waves do in our universe. (Somewhat more technically: most such graviton theories define them in terms of variations of the Ricci curvature tensor R_{\mu\nu}, much like we can describe a photon in terms of the electromagnetic tensor F_{\mu\nu}.)
So when-and-where does classical gravitational radiation appear?
Spherically symmetric static sources do not generate gravitational waves. However, if we raise a bump on such a source thus breaking both spherical a symmetry and staticity in favour of a dynamical bumpy spheroid -- then with a light-crossing time of the spherical source, the nearby external spacetime will have settled back down to a spherically symmetrical state. The near-region will also return to static (the curvature in the near-region stops varying) while at ever-further removes from the source one can find a perturbation in the curvature there-and-then.
This also works (although it takes much longer than about a light-crossing time) for objects which are slowly-rotating, roughly spherical, but not shrouded in a horizon. Such objects' bumps will eventually flatten, and the flattening is typically faster for more-massive bodies. We see this in the rocky bodies throughout the solar system. Gravitational radiation is shed during the flattening process, but at much lower amplitudes than on a bumpy black hole.
How do black holes get bumps? When something falls onto them. In particular, we study the collision of neutron stars and other black holes onto black holes at LIGO, Virgo, and soon other gravitational wave observatories. The more massive the infaller, the bigger the bump, and the larger the amplitude of the gravitational waves. Indeed, in several observations the black holes are of comparable mass, so they raise bumps on each other, and this can be seen in the multipole wave form.
Back to gravitons. A classical "chirp" of light can be seen as a large number of photons in the theories of quantum electrodynamics or of the Standard Model. A "chirp" of gravitational radiation detected at LIGO can be seen as a large number of gravitons in theories such as perturbative quantum gravity.
The spacetime outside but nearby a spherically symmetrical essentially-non-rotating object is boringly quiet, whether that object is a cold rocky body or a black hole. There won't be gravitational waves of non-negligible amplitude there. But if we induce a large perturbation by breaking that symmetry, the spacetime outside but near the object is much less boring, and filled with gravitational waves. That freshly-dynamical spacetime will eventually settle down, depending on the properties of its sources (the matter configuration), and thus eventually we get the nice quiet spacetime outside (but nearby) the body again. However, that's because the local gravitational perturbations have run away from the local area as gravitational waves.
A rocky body has a solid surface on which a solid bump can rest for very long times (but compare something that can melt or sublimate, deposited onto the surface of such a body). A black hole does not have a solid surface at the horizon: an infalling object passes right through the horizon. Some treatments (putting it very roughly) think about such an object very quickly melting and spreading all over the "surface" of the horizon. This is mathematically convenient sometimes, but conceptually misleading. The horizon cannot support anything -- nothing can rest on it. That's why the time it takes to flatten a bump on a black hole is about the light-crossing time of the black hole.
However, the gravitational radiation comes from the dynamical spacetime outside the horizon at the time the perturbation is raised. Once things settle down, there is just a bigger horizon.
Not covered above: extremely fast black hole rotation, such that we don't have sphericity or staticity in the first place. This doesn't really change the picture much: an infaller raises a bump, the bump is dragged around because of rotation, and settles down. The spacetime outside the rotating black hole with the bump is enormously dynamical, and emits gravitational waves, which fly away from the rotating black hole. In short order, even to observers many galaxies away (e.g. at LIGO), the spacetime around the perturbed rotating black hole will have settled down. Again, if there are gravitons, LIGO-like observers see enormous numbers of them all at once.
Also not covered above: black hole evaporation. We've never detected this, and might not be able to for up to trillions of years (before that we'd need there to have been small primordial black holes older than even any of the electrons in the universe). There is no full answer for what we should expect to see when the amplitude of gravitational radiation is likely to be high (during final evaporation). This is about the only time when what fell into the black hole over the course of its existence is likely to be relevant -- it likely would determine the spectrum of the gravitational radiation, but that radiation would originate in the near region of highly-dynamical spacetime just outside the shrinking horizon.
Penultimately: there are some really different graviton-containing theories that might describe aspects of our universe (even if they are defined for universes with many more spatial dimensions than the 3 that sufficiently describe all our physical observations to date). However, most really different theories have such different large-scale behaviours that there is no hope of connecting them with e.g. the central black hole of our galaxy.
Finally: one could build a tortured metaphor using a steel ball and blowtorch: heat one spot on the ball until it's glowing red, then switch off the blowtorch. It will have a definite localized hot spot -- a temperature bump -- that is visible from some angles but not others. Eventually the ball will thermalize: it will be essentially the same (cooling) temperature from every angle outside it, with no single glowing hotspot. The glow is the emission of a large number of electromagnetic waves (and those are large numbers of photons) carrying away the energetic perturbation on the sphere.
That's all well and good, but which part should I read to understand how gravitons travel from inside the event horizon to outside of it? Or maybe your response is a nice way of saying that the question is flawed and gravitons don't actually do that or don't need to do that?
The question isn't flawed, but ignoring final evaporation, nothing crosses from inside the horizon to outside. Nothing. Ever. Under any circumstances. Things can only move from the outside to the inside, unidirectionally, and on a one-way trip.
Gravitational radiation originates outside the horizon. It's noise in the near-horizon region caused by massive/energetic objects moving around outside the horizon (e.g. as a neutron star plunges inwards), and most of it dissipates away to infinity (a fraction settles down and serves to make a bigger, flatter horizon).
Gravitons in almost every physical theory that has them are simply what you get when you look very very closely at gravitational radiation like this, just as photons are what you get when you look very very closely at a bright flash of light.
Final evaporation isn't something we need to worry about for any practical purposes (and additionally it might never happen). However, just prior to final evaporation an extremely hot, tiny, almost-fully-evaporated black hole would be surrounded by a near-horizon region of extremely dynamical spacetime, which would be the source of quite a lot of gravitational radiation (and thus gravitons); the influence of that gravitational radiation on the spacetime-filling fields of the Standard Model would also generate quite a lot of electromagnetic (and other) radiation too. If we look very closely at all these different forms of radiation we'd see lots and lots of particles. That is, you might see X-rays and gamma rays, but they are not crossing from inside the horizon to outside. They're the effect of locally strongly curved spacetime on the local parts of universe-filling quantum fields (and the intense interactions of field-content being stretched and squashed in turn induces a backreaction on the dynamical spacetime nearby).
Thank you for the follow up. I've asked this question throughout the years and this is the first time that virtual grativitons haven't been introduced to explain away information escaping the event horizon. Thanks for taking the time to go through a thoughtful explanation.
It was an interesting distinction IMO, because if you think about it a lot of confusion comes when people think about gravity as a discrete thing that actually exists, when in fact gravity is merely a description of the effects that come with spacetime curvature.
Since you answered: do you have a good way to visualize the curvature of spacetime? I really don't understand how to think about light-cones being distorted, because it's the curvature of a lorentzian manifold that stiches together light cones with distortion.
If you can only visualize curvature of a 2D surface (embedded in the 3D space), you have to imagine the space as being 1D. I don't know of any other way.
Gravity does not travel at the speed of light. Some speculate that instant (ie: faster than light) communication could be possible by manipulating gravity.
How does gravity escape from a black hole? It, like light, travels at the speed of light. So if light cannot escape, how does gravity?