5 ms·

Or read Susskind's "The Theoretical Minimum: General Relativity". For a non-spinning blackhole at least, not only is the singularity not a point, it is a surfac

by kwoff 22d ago

Or read Susskind's "The Theoretical Minimum: General Relativity". For a non-spinning blackhole at least, not only is the singularity not a point, it is a surface in time, not space (as the book explains, the space and time coordinates switch places as you cross the event horizon).

dash2 22d ago
> the space and time coordinates switch places as you cross the event horizon I'm sorry but this is blowing my mind. What???
- lstodd 22d ago
  Yup. It's that weird. Also read Nick Gorkavyi: The Oscillating Universe: Einsteinian Cosmology of Black Holes and Gravitational Waves
- MathMonkeyMan 22d ago
  [This video][1] and the one before it on the playlist are a good no nonsense explanation of the topic. [1]: https://www.youtube.com/watch?v=O_2vnb_eVGE https://www.youtube.com/watch?v=O_2vnb_eVGE
- metalliqaz 22d ago
  it might help to think of the singularity as not a point in space but rather a future that cannot be avoided. All possible paths through space and time, no matter what happens, will go towards the singularity.
- Kranar 22d ago
  Because it's very misleading. Time and space do not switch places past the event horizon. What happens is that the direction/path between an object and the singularity becomes a timelike dimension, and the direction that plays the role of time outside of the event horizon becomes a spacelike dimension. That is not the same as them swapping or that time becomes space and space becomes time not to mention that space has 3 dimensions and time has only 1 dimension so how could they even swap places. Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time, specifically the amount of time left before you reach the singularity. It's not so mind blowing when you interpret it that way now is it? You can imagine many things in ordinary life that you use to measure time without claiming that time has literally swapped places with it. On a road trip, the number of kilometres to your exit tells you how long you have left, that's using space as a proxy for time... big deal. The notable difference between a road trip and a black hole is that on a road trip you could stop for a break, you could maybe take a detour, you could decide to go back home... and these would all break your use of space as a proxy for measuring time. Well with a blackhole you can't do any of those things, there is no going back, there is no detour, the relationship between the spatial direction towards the singularity and time is fixed and causal and there's nothing you can do about it. The phrasing used is used almost certainly to evoke some kind of voodoo mind-blowing mystery that completely disappears when you get down to the more strict formalism.
  - pdonis 22d ago
    > Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time That's not correct. There is a relationship between the radial coordinate r you are at and the time it will take you, by your clock, to reach the singularity (at least assuming you are freely falling), but that relationship can't be described the way you are describing it. To put the issue with what you say as starkly as possible: at any event inside the black hole's horizon, there are spacelike curves in every direction from you that will hit the singularity! So "the direction in space between you and the singularity" is not even well-defined. To be clear, you are right that Susskind's statement is very misleading (I posted my own criticism of it upthread).
    - jimberlage 22d ago
      Am I understanding this right by thinking - if I was walking toward the black hole past the event horizon, and then I turned around, I would still be walking toward the black hole?
      - HappMacDonald 22d ago
        Once you pass the event horizon, every direction leads to the singularity in your future. Directions "away" from the singularity may still visibly show what things looked like outside of the event horizon before you fell in, but that is from your past. Heading in that direction will not get you back there anymore, you will only find the singularity along that path in your future.
      - aqfamnzc 22d ago
        Sounds like that would be true if you were inside any closed surface.
        XorNot 22d ago
        Not quite: inside a closed surface you can't escape, but things can repeat. You can avoid a coordinate, for example by choosing not to go there, or revisit another one repeatedly. A black hole on the other hand doesn't have that: you cannot revisit old locations - attempting to do so moves you closer to the singularity.
- deleted 22d ago
  [deleted]
- _moof 22d ago
  It's unfortunately misleading shorthand for what actually happens: space becomes timelike. It doesn't become time. All this means is that once you cross the event horizon, you can only ever move toward the center of the black hole, in the same way that outside of a black hole, you can only ever move toward the future. You might not take a direct route to the center, but no matter which way you move, you will be following a track that ends at the center. The reason this phenomenon has a spooky-sounding name is that it also affects whether two objects can be causally connected. If you can only ever move closer to the center of the black hole, then there are (conceivably) other objects inside the event horizon that you can never have a causal relationship with. But it doesn't mean that space and time literally switch places.
pdonis 22d ago
> the space and time coordinates switch places as you cross the event horizon If Susskind's book does in fact say that, it's extremely disappointing to me, because, as a number of other GR textbooks will tell you (e.g., Misner, Thorne & Wheeler and Wald, the two great classic GR textbooks), the "switch places" is an artifact of a particular choice of coordinates (Schwarzschild coordinates), and does not represent anything physical. So it's not something that should be relied on. (Not to mention the confusion it causes when pop science sources repeat the statement and then draw all manner of wrong conclusions from it.) The part about being "a surface in time" might be all right, assuming that by that he means "a surface representing a moment in time, not a place in space"--in more technical language, a spacelike surface. That is correct, and it's an invariant that does not depend on any choice of coordinates. But that invariant fact can be described without having to talk about the "switch places" thing at all.
- kwoff 22d ago
  Susskind's book does also mention that the event-horizon shenanigans are due to coordinates and not a physical thing. Certainly I'd trust what he says rather than me, so sorry if I was misleading. (If anyone has the book, it is chapter 6 section "Interchange of Space and Time Dimensions at the Horizon" and the following section points out the singularity is a time (and you can't escape it (in a Schwartzschild model at least) just like you can't escape time). I'm sorry if my wording is still incorrect.).
  - pdonis 22d ago
    > Susskind's book does also mention that the event-horizon shenanigans are due to coordinates and not a physical thing. That's good. However: > Interchange of Space and Time Dimensions at the Horizon This still seems misleading to me, because "Dimensions" makes it seem like it's not just an artifact of coordinates--but it is.
- sigmoid10 22d ago
  Kruskal-Szeres coordinates indeed get rid of the wonky coordinate stuff at the event horizon, but if you look at the corresponding diagrams, you'll just end up with the same confusion, because the singularity is still a point (or rather surface) in the future instead of a point in space. The issue is that these diagrams are for eternal, static black holes, which cause diagrams to have these weirdly stretched infinite regions that are quite useful for understanding details of the math, but are highly confusing to laypeople. In fact these diagrams make it look like you'll always fall into the black hole at t=infinity, no matter how far you are away, when in reality you could orbit a static black hole pretty close for eternity. If you really want to get a picture of what is happening, you can look at Eddington-Finkelstein coordinates. In particular at a light cone field diagram around a collapsing shell of matter that turns into a black hole. Then this whole stuff suddenly makes sense without even going into the math. You don't just see how an event horizon can form out of nothing, you also see how gravity starts to bend your causal forward light cone (i.e. all points in spacetime with events that you could interact with in the future) inward in such a way that you will necessarily always fall closer to the center of the mass once you pass a certain line (aka the event horizon). No need to deal with those weird infinities or points in time suddenly lying on a different axis. The great Roger Penrose (the same guy who also came up with some of the most confusing diagrams) published a beautiful, simple overview of exactly this stuff in Scientific American: https://www.wkbpic.com/wkbx/SA/1972/1972-05-01.pdf https://www.wkbpic.com/wkbx/SA/1972/1972-05-01.pdf (starting on page 38) Still one of the best things you can read if you don't just want the math.
SoftTalker 22d ago
The way Brian Cox puts it, a singularity is a point in time: the end of time. I have trouble really conceptualizing black hole physics, I just think of it as a mass so great that nothing, including light, can escape its gravity. Works for me.
- XorNot 22d ago
  The more interesting component is that black hole physics is almost an anti-free will zone. Everywhere else in the universe with mass and energy you can do what you want (sort of). An event horizon throws a hard shroud over that and drastically reduces opportunities: your free will to use mass and energy is significantly curtailed (you must head towards the singularity).
  - teamonkey 22d ago
    I’m not sure free will has anything to do with it. If you don’t have enough upward velocity to escape earths gravity, hitting the ground is also inevitable.
  - Sharlin 22d ago
    Your free will outside a black hole is curtailed in exactly the same manner: you cannot do anything to avoid, or even delay, tomorrow.
    - XorNot 19d ago
      Which is exactly my point. Under normal circumstances you inexorably move towards the future. But we generally believe we have freedom of action about the spatial coordinates. A black hole is interesting because you inexorably move towards the singularity - which is a defined location in spacetime, and also has a boundary - the event horizon. So now your freedom of action is reduced: you must move towards the singularity, but you also can't actually move outside of the event horizon either.
- PaulHoule 22d ago
  The singularity in a non-rotating, non-charged black hole is as you say. It’s like in a finite amount of time you “run out of time”, like there isn’t any more time on that trajectory. The singularity in a rotating black hole is entirely different but the interior of classical Kerr (rotating) black holes is one of the most controversial if inconsequential topics in theoretical physics because there are reasons to believe (without real proof mind you) the Kerr solution is unstable inside the inner event horizon so that whatever happens in there is not what that theory says. And of course black holes are quantum objects which might actually have an “interior” entirely different from the classical picture.

by kwoff 22d ago

dash2 22d ago

> the space and time coordinates switch places as you cross the event horizon I'm sorry but this is blowing my mind. What???

lstodd 22d ago
Yup. It's that weird. Also read Nick Gorkavyi: The Oscillating Universe: Einsteinian Cosmology of Black Holes and Gravitational Waves
MathMonkeyMan 22d ago
[This video][1] and the one before it on the playlist are a good no nonsense explanation of the topic. [1]: https://www.youtube.com/watch?v=O_2vnb_eVGE https://www.youtube.com/watch?v=O_2vnb_eVGE
metalliqaz 22d ago
it might help to think of the singularity as not a point in space but rather a future that cannot be avoided. All possible paths through space and time, no matter what happens, will go towards the singularity.
Kranar 22d ago
Because it's very misleading. Time and space do not switch places past the event horizon. What happens is that the direction/path between an object and the singularity becomes a timelike dimension, and the direction that plays the role of time outside of the event horizon becomes a spacelike dimension. That is not the same as them swapping or that time becomes space and space becomes time not to mention that space has 3 dimensions and time has only 1 dimension so how could they even swap places. Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time, specifically the amount of time left before you reach the singularity. It's not so mind blowing when you interpret it that way now is it? You can imagine many things in ordinary life that you use to measure time without claiming that time has literally swapped places with it. On a road trip, the number of kilometres to your exit tells you how long you have left, that's using space as a proxy for time... big deal. The notable difference between a road trip and a black hole is that on a road trip you could stop for a break, you could maybe take a detour, you could decide to go back home... and these would all break your use of space as a proxy for measuring time. Well with a blackhole you can't do any of those things, there is no going back, there is no detour, the relationship between the spatial direction towards the singularity and time is fixed and causal and there's nothing you can do about it. The phrasing used is used almost certainly to evoke some kind of voodoo mind-blowing mystery that completely disappears when you get down to the more strict formalism.
- pdonis 22d ago
  > Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time That's not correct. There is a relationship between the radial coordinate r you are at and the time it will take you, by your clock, to reach the singularity (at least assuming you are freely falling), but that relationship can't be described the way you are describing it. To put the issue with what you say as starkly as possible: at any event inside the black hole's horizon, there are spacelike curves in every direction from you that will hit the singularity! So "the direction in space between you and the singularity" is not even well-defined. To be clear, you are right that Susskind's statement is very misleading (I posted my own criticism of it upthread).
  - jimberlage 22d ago
    Am I understanding this right by thinking - if I was walking toward the black hole past the event horizon, and then I turned around, I would still be walking toward the black hole?
    - HappMacDonald 22d ago
      Once you pass the event horizon, every direction leads to the singularity in your future. Directions "away" from the singularity may still visibly show what things looked like outside of the event horizon before you fell in, but that is from your past. Heading in that direction will not get you back there anymore, you will only find the singularity along that path in your future.
    - aqfamnzc 22d ago
      Sounds like that would be true if you were inside any closed surface.
      - XorNot 22d ago
        Not quite: inside a closed surface you can't escape, but things can repeat. You can avoid a coordinate, for example by choosing not to go there, or revisit another one repeatedly. A black hole on the other hand doesn't have that: you cannot revisit old locations - attempting to do so moves you closer to the singularity.
deleted 22d ago
[deleted]
_moof 22d ago
It's unfortunately misleading shorthand for what actually happens: space becomes timelike. It doesn't become time. All this means is that once you cross the event horizon, you can only ever move toward the center of the black hole, in the same way that outside of a black hole, you can only ever move toward the future. You might not take a direct route to the center, but no matter which way you move, you will be following a track that ends at the center. The reason this phenomenon has a spooky-sounding name is that it also affects whether two objects can be causally connected. If you can only ever move closer to the center of the black hole, then there are (conceivably) other objects inside the event horizon that you can never have a causal relationship with. But it doesn't mean that space and time literally switch places.

pdonis 22d ago

> the space and time coordinates switch places as you cross the event horizon If Susskind's book does in fact say that, it's extremely disappointing to me, because, as a number of other GR textbooks will tell you (e.g., Misner, Thorne & Wheeler and Wald, the two great classic GR textbooks), the "switch places" is an artifact of a particular choice of coordinates (Schwarzschild coordinates), and does not represent anything physical. So it's not something that should be relied on. (Not to mention the confusion it causes when pop science sources repeat the statement and then draw all manner of wrong conclusions from it.) The part about being "a surface in time" might be all right, assuming that by that he means "a surface representing a moment in time, not a place in space"--in more technical language, a spacelike surface. That is correct, and it's an invariant that does not depend on any choice of coordinates. But that invariant fact can be described without having to talk about the "switch places" thing at all.

kwoff 22d ago
Susskind's book does also mention that the event-horizon shenanigans are due to coordinates and not a physical thing. Certainly I'd trust what he says rather than me, so sorry if I was misleading. (If anyone has the book, it is chapter 6 section "Interchange of Space and Time Dimensions at the Horizon" and the following section points out the singularity is a time (and you can't escape it (in a Schwartzschild model at least) just like you can't escape time). I'm sorry if my wording is still incorrect.).
- pdonis 22d ago
  > Susskind's book does also mention that the event-horizon shenanigans are due to coordinates and not a physical thing. That's good. However: > Interchange of Space and Time Dimensions at the Horizon This still seems misleading to me, because "Dimensions" makes it seem like it's not just an artifact of coordinates--but it is.
sigmoid10 22d ago
Kruskal-Szeres coordinates indeed get rid of the wonky coordinate stuff at the event horizon, but if you look at the corresponding diagrams, you'll just end up with the same confusion, because the singularity is still a point (or rather surface) in the future instead of a point in space. The issue is that these diagrams are for eternal, static black holes, which cause diagrams to have these weirdly stretched infinite regions that are quite useful for understanding details of the math, but are highly confusing to laypeople. In fact these diagrams make it look like you'll always fall into the black hole at t=infinity, no matter how far you are away, when in reality you could orbit a static black hole pretty close for eternity. If you really want to get a picture of what is happening, you can look at Eddington-Finkelstein coordinates. In particular at a light cone field diagram around a collapsing shell of matter that turns into a black hole. Then this whole stuff suddenly makes sense without even going into the math. You don't just see how an event horizon can form out of nothing, you also see how gravity starts to bend your causal forward light cone (i.e. all points in spacetime with events that you could interact with in the future) inward in such a way that you will necessarily always fall closer to the center of the mass once you pass a certain line (aka the event horizon). No need to deal with those weird infinities or points in time suddenly lying on a different axis. The great Roger Penrose (the same guy who also came up with some of the most confusing diagrams) published a beautiful, simple overview of exactly this stuff in Scientific American: https://www.wkbpic.com/wkbx/SA/1972/1972-05-01.pdf https://www.wkbpic.com/wkbx/SA/1972/1972-05-01.pdf (starting on page 38) Still one of the best things you can read if you don't just want the math.

SoftTalker 22d ago

The way Brian Cox puts it, a singularity is a point in time: the end of time. I have trouble really conceptualizing black hole physics, I just think of it as a mass so great that nothing, including light, can escape its gravity. Works for me.

XorNot 22d ago
The more interesting component is that black hole physics is almost an anti-free will zone. Everywhere else in the universe with mass and energy you can do what you want (sort of). An event horizon throws a hard shroud over that and drastically reduces opportunities: your free will to use mass and energy is significantly curtailed (you must head towards the singularity).
- teamonkey 22d ago
  I’m not sure free will has anything to do with it. If you don’t have enough upward velocity to escape earths gravity, hitting the ground is also inevitable.
- Sharlin 22d ago
  Your free will outside a black hole is curtailed in exactly the same manner: you cannot do anything to avoid, or even delay, tomorrow.
  - XorNot 19d ago
    Which is exactly my point. Under normal circumstances you inexorably move towards the future. But we generally believe we have freedom of action about the spatial coordinates. A black hole is interesting because you inexorably move towards the singularity - which is a defined location in spacetime, and also has a boundary - the event horizon. So now your freedom of action is reduced: you must move towards the singularity, but you also can't actually move outside of the event horizon either.
PaulHoule 22d ago
The singularity in a non-rotating, non-charged black hole is as you say. It’s like in a finite amount of time you “run out of time”, like there isn’t any more time on that trajectory. The singularity in a rotating black hole is entirely different but the interior of classical Kerr (rotating) black holes is one of the most controversial if inconsequential topics in theoretical physics because there are reasons to believe (without real proof mind you) the Kerr solution is unstable inside the inner event horizon so that whatever happens in there is not what that theory says. And of course black holes are quantum objects which might actually have an “interior” entirely different from the classical picture.