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Black hole singularity is a surface not a point

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Re: Black hole singularity is a surface not a point

#81

Post by dhosek »

sigmoid10 wrote: post #2

Should be pointed out that this is a critique of common popsci journalism tropes and not a fancy new research result. Anyone who has taken a graduate level class in General Relativity would have been able to tell you the same.

I figure at least some of it comes from the idea that mathematically, a singularity is a point (e.g., in the graph of z=1/w, there is a singularity at the point w=0, and in the graph of z=(1-w)²/(1-w) there is a removable singularity at w=1 (that is, the function is undefined at w=1, but if you put a point at (1,0), the graph will be continuous and no longer have any holes in it). The fact that both have the same name and the similar behavior of a black hole singularity to a mathematical singularity¹ can lead people to make an incorrect assumption.

⸻

1. I must admit to a lack of sufficient GR education to feel confident in this, but I think that one of the issues that made physicists unwilling to accept the idea of black holes when they were first postulated was that there ended up being a division by zero in the mathematics.

Re: Black hole singularity is a surface not a point

#82

Post by XorNot »

sigmoid10 wrote: post #61
pdonis wrote: post #43

Earlier quoted context omitted.

> 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 any…

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…

This doesn't seem meaningfully different to me? Like the notion that the singularity is always in your future (because you can't escape it anymore past the event horizon) makes sense, the point of confusion is what are the implications?

Roughly the general public (including me) knows that gravity is meant to have some effect on the apparent passage of time, so it seems significant but under explained what it means to be in a region of space where all possible directions lead to the singularity.

Re: Black hole singularity is a surface not a point

#83

Post by pdonis »

jimberlage wrote: post #55
pdonis wrote: post #48

Earlier quoted context omitted.

> 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.…

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?

> if I was walking toward the black hole past the event horizon, and then I turned around

Note that, once you're inside the horizon, you can't "turn around" and go back outside again. You're inside the hole for good.

And once you're inside the hole, yes, no matter which direction in space you move, you're moving "towards" the singularity. But a better way to look at it is that the singularity is a moment of time, not a place in space. You're moving "towards" the singularity in the same sense as you're moving "towards" next Tuesday. You can't stop moving towards next Tuesday by changing which direction in space you move. The same is true for the singularity once you're inside the hole's horizon.

Re: Black hole singularity is a surface not a point

#84

Post by XorNot »

SoftTalker wrote: post #67
kwoff wrote: post #12

Earlier quoted context omitted.

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).

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.

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).

Re: Black hole singularity is a surface not a point

#85

Post by PaulHoule »

goatlover wrote: post #68
rf15 wrote: post #57

Earlier quoted context omitted.

As someone with basically only popsci knowledge of black holes: people claiming it would be a literal point never made much sense - fundamentally, common sense (as much as it can apply here) dictates that you cannot compress particles to an absolute point.

Aren't fundamental particles like electrons and quarks treated as points?

If you really treated them as points the theory would blow up because the electrostatic potential energy of a point charge is infinite. This is dealt with by “renormalization” which is roughly: assume the theory isn’t really valid all the way to a zero length scale and that we can average out everything that happens below some cutoff size and that it doesn’t really matter where we place the cutoff because the theory works the same if you change the cutoff and change the other parameters accordingly.

Re: Black hole singularity is a surface not a point

#86

Post by pdonis »

sigmoid10 wrote: post #61
pdonis wrote: post #43

Earlier quoted context omitted.

> 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 any…

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…

> the singularity is still a point (or rather surface) in the future instead of a point in space.

It's a spacelike line on the Kruskal diagram, yes.

> The issue is that these diagrams are for eternal, static black holes

The full Kruskal diagram is, yes. But the essential features of the black hole portion of that diagram are still there in a black hole that forms by gravitational collapse of a massive body. That includes the singularity being a spacelike line, and there being spacelike curves inside the horizon that are infinitely long.

I agree that Eddington-Finkelstein coordinates can help with intuitions about this spacetime geometry as well.

Re: Black hole singularity is a surface not a point

#87

Post by pdonis »

XorNot wrote: post #82
sigmoid10 wrote: post #61

Earlier quoted context omitted.

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…

This doesn't seem meaningfully different to me? Like the notion that the singularity is always in your future (because you can't escape it anymore past the event horizon) makes sense, the point of confusion is what are the implications? Roughly the general public (including me) knows that gravity is meant to have some effect on the apparent passage of time, so it seems significant but under explained what it means to…

> the singularity is always in your future

It's not just that it's always in your future in the sense that you can't avoid it. It's that the reason you can't avoid it is that it's a moment of time, not a place in space. You can't avoid it for the same reason you can't avoid tomorrow. And which direction in space you move has no effect on whether or not you reach the singularity for the same reason it has no effect on whether or not you reach tomorrow.

Re: Black hole singularity is a surface not a point

#88

Post by XorNot »

aqfamnzc wrote: post #66
jimberlage wrote: post #55

Earlier quoted context omitted.

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?

Sounds like that would be true if you were inside any closed surface.

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.

Re: Black hole singularity is a surface not a point

#89

Post by pdonis »

kwoff wrote: post #56
pdonis wrote: post #43

Earlier quoted context omitted.

> 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 any…

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 a…

> 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.

Re: Black hole singularity is a surface not a point

#90

Post by sigmoid10 »

dhosek wrote: post #81
sigmoid10 wrote: post #2

Should be pointed out that this is a critique of common popsci journalism tropes and not a fancy new research result. Anyone who has taken a graduate level class in General Relativity would have been able to tell you the same.

I figure at least some of it comes from the idea that mathematically, a singularity is a point (e.g., in the graph of z=1/w, there is a singularity at the point w=0, and in the graph of z=(1-w)²/(1-w) there is a removable singularity at w=1 (that is, the function is undefined at w=1, but if you put a point at (1,0), the graph will be continuous and no longer have any holes in it). The fact that both have the same nam…

>The fact that both have the same name

They don't just have the same name, they are the same thing.

A Schwarzschild black hole has both: a removable singularity at the event horizon that is just an artefact of a particular choice of coordinates and a true non-removable mathematical singularity at r=0 where curvature really does go to infinity. It also wouldn't be much of an issue in classical physics, because this singularity is always hidden from outside observers, so the mathematical weirdness there can't screw with your normal predictions in space outside the black hole. The problems start once you consider quantum mechanics, because any such singularity will break unitarity (a fancy way of saying that probabilities must add up to 1), which means your theory as a whole can no longer make predictions. This has opened a whole can of worms with a bunch of solution attempts, which are all sadly untestable for the foreseeable future.

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