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What do you mean by "across the singularity"? The singularity is a single point in the center. There's no being across it really.

actionfromafar 4y ago
I'm sure that's right, but on the other hand space itself is getting "denser" nearer to the singularity. I don't know what to make of that.
- pdonis 4y ago
  > space itself is getting "denser" nearer to the singularity Where are you getting this from? It makes no sense.
zmgsabst 4y ago
When the shortest path lies on some sphere around the singularity where the circumference of that sphere is “quantum scale” but chords passing near the center are not. In the 2D example, is there some area where quantum effects happen in an annulus rather than in a disc because that central stretched region is “too big”.
- pdonis 4y ago
  > some sphere around the singularity There is no such thing. The singularity is a moment of time, not a place in space.
  - zmgsabst 4y ago
    The event horizon is an example of a sphere around the singularity. So is the photon sphere.
    - pdonis 4y ago
      No, this is not correct. The singularity is not a place in space, so it is not possible to have a sphere around it. It makes no sense, just as having a sphere around, say, tomorrow noon makes no sense.
      - zmgsabst 4y ago
        Perhaps instead of just saying what standard explanations are “make no sense”, you could try elaborating in any of your posts. Saying that an event horizon or photon sphere isn’t around the singularity of a black hole doesn’t make sense, either. What facts specifically are you trying to articulate about spacetime geometry around a black hole?
        pdonis 4y ago
        > you could try elaborating in any of your posts I already have: the singularity is a moment of time, not a place in space. > Saying that an event horizon or photon sphere isn’t around the singularity of a black hole doesn’t make sense, either. Yes, it does, for the reason I've already given: because there is no such thing as a sphere around a moment of time. > What facts specifically are you trying to articulate about spacetime geometry around a black hole? The fact that the singularity is not a place in space, it's a moment of time.
        zmgsabst 4y ago
        A singularity is a point on a spacetime manifold where it has a cusp. You can draw a bounding sphere around that, of which I’ve given two examples. What fact about spacetime geometries are you trying to convey? You should try explaining the relevance of what you’re repeating in terms of spacetime geometries rather than just repeating the same statement over and over — which isn’t a constructive reply.
        pdonis 4y ago
        > A singularity is a point on a spacetime manifold where it has a cusp. No, it isn't. At least not in GR (perhaps your definition is valid in some other context). In GR, a singularity is present in a spacetime if the spacetime has non-extendable geodesics. Strictly speaking, the singularity itself is not even part of the spacetime manifold; but if we attach it to the spacetime manifold as a sort of boundary, it does not have to be a point. In the case of the singularity at r = 0 in Schwarzschild spacetime, the singularity is a spacelike line which is to the future of all events inside the hole. No geodesics can be extended past that line because spacetime curvature increases without bound as it is approached (and curvature is "infinite" on the line itself, which is why the line itself is not and cannot be part of the spacetime manifold, since curvature invariants must be finite everywhere on the manifold). > You should try explaining the relevance of what you’re repeating in terms of spacetime geometries What I am saying is a well known property of a well known solution in GR. I am describing it in as non-technical language as I can. Perhaps what I said above will help.
pdonis 4y ago
> The singularity is a single point in the center. No, it isn't. It's a spacelike line that is to the future of every event inside the hole. It's a moment of time, not a place in space.

actionfromafar 4y ago

I'm sure that's right, but on the other hand space itself is getting "denser" nearer to the singularity. I don't know what to make of that.

pdonis 4y ago
> space itself is getting "denser" nearer to the singularity Where are you getting this from? It makes no sense.

zmgsabst 4y ago

When the shortest path lies on some sphere around the singularity where the circumference of that sphere is “quantum scale” but chords passing near the center are not. In the 2D example, is there some area where quantum effects happen in an annulus rather than in a disc because that central stretched region is “too big”.

pdonis 4y ago
> some sphere around the singularity There is no such thing. The singularity is a moment of time, not a place in space.
- zmgsabst 4y ago
  The event horizon is an example of a sphere around the singularity. So is the photon sphere.
  - pdonis 4y ago
    No, this is not correct. The singularity is not a place in space, so it is not possible to have a sphere around it. It makes no sense, just as having a sphere around, say, tomorrow noon makes no sense.
    - zmgsabst 4y ago
      Perhaps instead of just saying what standard explanations are “make no sense”, you could try elaborating in any of your posts. Saying that an event horizon or photon sphere isn’t around the singularity of a black hole doesn’t make sense, either. What facts specifically are you trying to articulate about spacetime geometry around a black hole?
      - pdonis 4y ago
        > you could try elaborating in any of your posts I already have: the singularity is a moment of time, not a place in space. > Saying that an event horizon or photon sphere isn’t around the singularity of a black hole doesn’t make sense, either. Yes, it does, for the reason I've already given: because there is no such thing as a sphere around a moment of time. > What facts specifically are you trying to articulate about spacetime geometry around a black hole? The fact that the singularity is not a place in space, it's a moment of time.
        zmgsabst 4y ago
        A singularity is a point on a spacetime manifold where it has a cusp. You can draw a bounding sphere around that, of which I’ve given two examples. What fact about spacetime geometries are you trying to convey? You should try explaining the relevance of what you’re repeating in terms of spacetime geometries rather than just repeating the same statement over and over — which isn’t a constructive reply.
        pdonis 4y ago
        > A singularity is a point on a spacetime manifold where it has a cusp. No, it isn't. At least not in GR (perhaps your definition is valid in some other context). In GR, a singularity is present in a spacetime if the spacetime has non-extendable geodesics. Strictly speaking, the singularity itself is not even part of the spacetime manifold; but if we attach it to the spacetime manifold as a sort of boundary, it does not have to be a point. In the case of the singularity at r = 0 in Schwarzschild spacetime, the singularity is a spacelike line which is to the future of all events inside the hole. No geodesics can be extended past that line because spacetime curvature increases without bound as it is approached (and curvature is "infinite" on the line itself, which is why the line itself is not and cannot be part of the spacetime manifold, since curvature invariants must be finite everywhere on the manifold). > You should try explaining the relevance of what you’re repeating in terms of spacetime geometries What I am saying is a well known property of a well known solution in GR. I am describing it in as non-technical language as I can. Perhaps what I said above will help.

pdonis 4y ago

> The singularity is a single point in the center. No, it isn't. It's a spacelike line that is to the future of every event inside the hole. It's a moment of time, not a place in space.