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As I interpreted it, it's a diagram of a lab falling through a horizon, as viewed by someone at rest with respect to the lab. The horizon would be a plane trave

• pdonis 14y ago
  The horizon would be a plane traversing the lab No, it wouldn't. That's the point. The horizon is an outgoing lightlike surface; with respect to Frame X (or to any inertial frame that straddles the horizon), it's moving radially outward at the speed of light. It's not a plane stationary in space. The singularity would be in one direction perpendicular to the horizon No, it wouldn't. The singularity is to the future of the horizon; the direction from the horizon to the singularity is timelike, not spacelike. There's a coffee mug in front of me now. Regardless whether it's a spacelike or timelike direction, the mug is in that direction. This is not correct; timelike directions are fundamentally different from spacelike directions. What direction is next Tuesday from you now? That's a timelike direction, and it's not the same direction as the direction of a coffee mug, or any object that is in the space around you now. It's not even the same kind of direction. But that kind of direction--the kind that next Tuesday is in from you now--is the direction the singularity is in from the horizon. I'm not seeing a problem with the diagram. That's because you evidently don't understand what the curved spacetime around a black hole is like. It's a perfectly self-consistent model; but it doesn't work the way the web page author, and evidently you, think it works.
  • genwin 14y ago
    > The horizon is an outgoing lightlike surface; with respect to Frame X (or to any inertial frame that straddles the horizon), it's moving radially outward at the speed of light. It's not a plane stationary in space. "Lightlike surface" and plane are not incompatible ideas. Surface = plane in this case. The diagram or its caption doesn't say the horizon is stationary, it says the frame is falling through the horizon. Presumably the horizon is indeed moving in that frame at the speed of light (an outgoing lightlike surface). > What direction is next Tuesday from you now? The singularity is not a date; it's an object, like my coffee mug is. It's not invalid to show a direction to an object just because you'll reach the object next Tuesday. > That's because you evidently don't understand what the curved spacetime around a black hole is like. I've take a couple years of classes on this stuff. You're using the terminology inappropriately. The terms spacelike and timelike are not limited to black holes. By saying the diagram incorrectly shows the direction to the singularity you're implying that neither can I point to my coffee mug and say it's in that direction. But I can point to my coffee mug as validly as someone in frame X could point to the singularity. I can even point to a real purported singularity by walking outside and pointing to the direction of the center of the Milky Way. It's no more complex than that. Can I validly point to the center of the Milky Way? If yes, then there's no problem with the diagram in that regard. > It's a perfectly self-consistent model An assumption that should be set aside when considering an objection to it.
    • pdonis 14y ago
      Presumably the horizon is indeed moving in that frame at the speed of light If that's true, the the diagram that's shown cannot portray a steady state of Frame X, as it claims to do. At most it can show how things look in Frame X at a single instant of time. The horizon plane is moving to the right in the diagram at the speed of light, and none of the cloud particles can move at the speed of light, so the horizon plane will quickly overtake them and be to the right of the entire cloud. The argument in the text is not consistent with this. The singularity is not a date; it's an object, like my coffee mug is. No, the singularity is not an object like your coffee mug. That's the point. The singularity is a moment in time, not a place in space. If you don't know this then you need to do some review; it's a basic fact about the black hole solution in General Relativity. I've take a couple years of classes on this stuff. What material have you covered? Have you specifically covered the Schwarzschild solution to the Einstein Field Equation, and the description of it in the Kruskal coordinate chart? (Or the Painleve chart, or the Eddington-Finkelstein chart, or any other chart which is not singular at the horizon?) If not, I suggest you wait until those things are covered, or read ahead in your course material. You're using the terminology incorrectly. The terms spacelike and timelike are not limited to black holes. I didn't say they were. You're correct, they are general terms describing different kinds of directions in spacetime. ("Lightlike" or "null" is the third kind of direction.) A black hole is a spacetime, therefore the terms apply in it, and I was using them correctly. Can I validly point to the center of the Milky Way? Sure, but you won't be pointing to the singularity in the center of the black hole there. Once again, that would be like pointing to next Tuesday--or, since the center of the galaxy is some thirty thousand light years from us, it would be like pointing to a moment thirty thousand years or more into your future. An assumption that should be set aside when considering an objection to it. Only if the purported criticism represents the model correctly. It doesn't.