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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 even

by XorNot 1mo ago

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.

pdonis 1mo ago
> 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.
sigmoid10 1mo ago
>the notion that the singularity is always in your future makes sense But it is just a mathematical artefact of weirdly chosen coordinates. In reality, the singularity is still just a point in space (or a line in spacetime), except that inside the event horizon all paths you are allowed to travel lead to it. There's no need for this whole "space turns into time" notion apart from the fact that you are guaranteed to hit it in *your* future as a local observer. And in Eddington-Finkelstein coordinates you can easily see that globally, things simply hit the spatial coordinates of the singularity at certain slices of coordinate time. Other coordinate systems make this whole process seem much more weird than it is.
- pdonis 1mo ago
  > it is just a mathematical artefact of weirdly chosen coordinates. No, that's not correct. The fact that the singularity is always in your future inside the horizon is an invariant, independent of any choice of coordinates. > the singularity is still just a point in space No, it's not. A point in space would be a timelike line in spacetime. But the singularity is a spacelike line in spacetime. That's a moment of time, not a place in space. > There's no need for this whole "space turns into time" notion That's true; that notion is an artifact of Schwarzschild coordinates. But that does not imply the other claims you are making. > the spatial coordinates of the singularity I'm not sure what you mean by this. It's true that, since the singularity is a spacelike line, you can treat a coordinate that varies along it as a "spatial" coordinate marking different spatial points on the singularity. But the singularity itself is a moment of time (as above, a spacelike line), so it is not a "place", and it does not have a particular set of "spatial coordinates". A spatial coordinate marking different points along the singularity is marking different points in space at a moment of time.
  - sigmoid10 1mo ago
    Just draw the geometry in Eddington Finkelstein coordinates and you will see everything I wrote above is true at the technical level if you read precisely.
    - pdonis 1mo ago
      No, everything you wrote is not true, in Eddington Finkelstein or any other coordinates. You wrote that the singularity is a point in space. It's not, no matter what coordinates you choose. It's a line in spacetime, but it's a spacelike line, and a spacelike line cannot describe a point in space. It can only describe a moment of time. No choice of coordinates can change that. (Similar remarks apply to your claim that the singularity always being in your future once you're inside the horizon is an artifact of a coordinate choice. It's not. It's just as true in Eddington-Finkelstein coordinates, or any others.) That also makes your use of the term "spatial coordinates" questionable, as I already pointed out. The fact that the line r = 0 is vertical in an Eddington-Finkelstein spacetime diagram does not mean it's automatically a "point in space" or that r inside the horizon is automatically a "spatial coordinate". You need to look at the actual physics, not just the surface appearance of the diagram.
      - sigmoid10 1mo ago
        >You wrote that the singularity is a point in space Because it is. Remember: space, not spacetime. Hence the remark in brackets in the original comment and my reminder to read precisely in the other one. And in Eddington Finkelstein it is most obvious that it is a point in space (i.e. it has spatial coordinate r=0 where r has the metric signature of a spatial dimension) that you can hit at various points in (global) time (and actually also in free falling observer time, but let's ignore that since it is not immediately obvious). You can literally trace incoming light rays crossing the event horizon and hitting the singularity at r=0 at a certain points in time in the diagram. This stuff is really not that weird once you choose less confusing coordinates. It only gets weird once you start asking what local observers can actually see, because from their perspective their relation to all other coordinates in spacetime gets really messy. That's probably where 95% of the confusion among laypeople comes from. But for that you can still resort to other coordinates which show it much better.

by XorNot 1mo ago

pdonis 1mo ago

> 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.

sigmoid10 1mo ago

>the notion that the singularity is always in your future makes sense But it is just a mathematical artefact of weirdly chosen coordinates. In reality, the singularity is still just a point in space (or a line in spacetime), except that inside the event horizon all paths you are allowed to travel lead to it. There's no need for this whole "space turns into time" notion apart from the fact that you are guaranteed to hit it in *your* future as a local observer. And in Eddington-Finkelstein coordinates you can easily see that globally, things simply hit the spatial coordinates of the singularity at certain slices of coordinate time. Other coordinate systems make this whole process seem much more weird than it is.

pdonis 1mo ago
> it is just a mathematical artefact of weirdly chosen coordinates. No, that's not correct. The fact that the singularity is always in your future inside the horizon is an invariant, independent of any choice of coordinates. > the singularity is still just a point in space No, it's not. A point in space would be a timelike line in spacetime. But the singularity is a spacelike line in spacetime. That's a moment of time, not a place in space. > There's no need for this whole "space turns into time" notion That's true; that notion is an artifact of Schwarzschild coordinates. But that does not imply the other claims you are making. > the spatial coordinates of the singularity I'm not sure what you mean by this. It's true that, since the singularity is a spacelike line, you can treat a coordinate that varies along it as a "spatial" coordinate marking different spatial points on the singularity. But the singularity itself is a moment of time (as above, a spacelike line), so it is not a "place", and it does not have a particular set of "spatial coordinates". A spatial coordinate marking different points along the singularity is marking different points in space at a moment of time.
- sigmoid10 1mo ago
  Just draw the geometry in Eddington Finkelstein coordinates and you will see everything I wrote above is true at the technical level if you read precisely.
  - pdonis 1mo ago
    No, everything you wrote is not true, in Eddington Finkelstein or any other coordinates. You wrote that the singularity is a point in space. It's not, no matter what coordinates you choose. It's a line in spacetime, but it's a spacelike line, and a spacelike line cannot describe a point in space. It can only describe a moment of time. No choice of coordinates can change that. (Similar remarks apply to your claim that the singularity always being in your future once you're inside the horizon is an artifact of a coordinate choice. It's not. It's just as true in Eddington-Finkelstein coordinates, or any others.) That also makes your use of the term "spatial coordinates" questionable, as I already pointed out. The fact that the line r = 0 is vertical in an Eddington-Finkelstein spacetime diagram does not mean it's automatically a "point in space" or that r inside the horizon is automatically a "spatial coordinate". You need to look at the actual physics, not just the surface appearance of the diagram.
    - sigmoid10 1mo ago
      >You wrote that the singularity is a point in space Because it is. Remember: space, not spacetime. Hence the remark in brackets in the original comment and my reminder to read precisely in the other one. And in Eddington Finkelstein it is most obvious that it is a point in space (i.e. it has spatial coordinate r=0 where r has the metric signature of a spatial dimension) that you can hit at various points in (global) time (and actually also in free falling observer time, but let's ignore that since it is not immediately obvious). You can literally trace incoming light rays crossing the event horizon and hitting the singularity at r=0 at a certain points in time in the diagram. This stuff is really not that weird once you choose less confusing coordinates. It only gets weird once you start asking what local observers can actually see, because from their perspective their relation to all other coordinates in spacetime gets really messy. That's probably where 95% of the confusion among laypeople comes from. But for that you can still resort to other coordinates which show it much better.