5 ms·

The "surface area" of a black hole is defined precisely as the area of the boundary beyond which light cannot escape, so I don't this angle will work the way yo

by Steuard 13y ago

The "surface area" of a black hole is defined precisely as the area of the boundary beyond which light cannot escape, so I don't this angle will work the way you're thinking it might. (It's fairly straightforward to show that that surface does indeed expand as more mass is added, too.) It's pretty neat, actually: if you had a black hole containing the mass of a whole galaxy (which isn't unthinkable, especially in the distant future), local space-time at the event horizon would seem completely ordinary (at least as far as we understand from classical relativity and semi-classical quantum corrections like Hawking radiation). You wouldn't have the foggiest idea that you had crossed that fateful line... until you caught on to the fact that you weren't actually making any progress when you tried to turn back.

saalweachter 13y ago
This has always bothered me. I am not a point mass. If I can cross the event horizon and not know it, then there is a time when my feet are on one side and my head on the other. If signals cannot cross the event, how would I not notice my missing feet? If signals from my doomed feet can reach my not yet doomed head, then how is it the event horizon?
- rca 13y ago
  What if the signals emitted from inside the horizon do reach your head, but only once your head have crossed the horizon? Basically, you can change your reference point and consider that the signal is not moving, but your head is still moving towards the signal. This way, you're still seeing your legs. (Note that I have no idea what I'm talking about)
- Steuard 13y ago
  Well, your feet aren't ever "missing": as far as classical GR is concerned (even with Hawking's semi-classical quantum corrections included), your experience would be perfectly comfortable and unexceptional as you drifted in. The issue is that in that scenario, your head isn't on an escaping trajectory: the nerve signals from your feet might be moving "outward", but your head will be moving inward, and the signal will only get to your brain after your brain has also crossed the horizon. Now, if you were wearing some sort of rocket collar that fired powerfully just before your head crossed the horizon and carried it safely away from the black hole (or even just held it there), you're right: you wouldn't ever receive that signal from your feet. But I'm pretty sure that would be the least of your worries! (And you would notice your missing feet. And torso.) Roughly speaking, the only non-orbital trajectories close to an event horizon that don't fall straight in must be moving pretty close to light speed as seen by infalling observers.
  - codeflo 13y ago
    To state that point in another way, the key here is time dilation. (Please correct me if that's wrong.) Let's assume that your feet send a periodic signal to the brain, a "tingling" that let's you know your feet are still there. As your feet approach the event horizon, the tingling will get slower and slower, because time passes much faster for your head than for your feet. As your feet pass the event horizon, the tingling has become infinitely slow (relative to your head). But there's no sharp line where suddenly something happens as your feet touch the event horizon. (All of this of course only in principle and under the premise that you're not smashed to bits at that point.)
    - millstone 13y ago
      I would say this isn't quite right. It's true that time passes more slowly for your feet than your head, but this is due to tidal forces: your head and feet are different distances away from the black hole. For very large black holes, the tidal forces at the event horizon will be small, and the event horizon is the unexceptional, smooth spacetime that Steuard described. So in your example, for a large black hole, you will experience no difference in the rate of tingling as you cross the event horizon. This is what the principle of relativity tells us: you are in free fall, so the laws of physics must appear the same to you.
    - Steuard 13y ago
      I'm not sure that this captures the physics accurately from the perspective that you're describing here. The extreme time dilation that occurs as you approach a black hole's event horizon is really a "global" effect rather than a "local" one: it is defined by the relative difference in how time progresses close to the black hole vs. very far away. When you're falling through the horizon (particularly for a black hole so large that the tidal forces at the horizon aren't deadly), your whole body is "close", so there isn't substantial time dilation between your head and your feet. This is a little bit weird, I know!
    - pdonis 13y ago
      (Please correct me if that's wrong.) It's wrong. Time dilation is not something you observe yourself to experience; it's something another observer observes you to be experiencing. "Time" is relative, so you can feel your own time to be ticking away perfectly normally while it appears to be ticking much more slowly to someone else. As your feet approach the event horizon, the tingling will get slower and slower, because time passes much faster for your head than for your feet. No, this is not correct. As you fall toward and through the horizon, signals travel between your head and your feet just fine, and you don't notice any difference in how fast they travel. But, as I posted upthread, if your foot emits a signal towards your head when it's below the horizon and your head is above it, then by the time the signal reaches your head, your head will have fallen below the horizon.
- marcosdumay 13y ago
  Thinking about non-ponty masses on General Relativity makes me dizzy (no kidding, I'm quite sure I know the difference between being in a cenrifuge or on the surface of a planet), but you can take for granted that you'll be dead way before reaching the event horizon of a macroscopic black hole.
  - codeflo 13y ago
    Is it easier to think about point masses held together by invisible springs? The point masses being atoms, and the springs being electric fields. Not a perfect analogy, but it should work to visualize a lot of the macroscopic effects of gravity. BTW, it's not hard to convince yourself that masses and springs in a centrifuge behave exactly like those near a large body. (In Newtonian mechanics even.) How are you sure you know the difference?
- pdonis 13y ago
  If signals cannot cross the event, how would I not notice my missing feet? If your feet are below the horizon and your head is above it, then you must be falling through the horizon; it's impossible to remain at a constant altitude at the horizon, even for an instant. So a signal emitted by your foot would still reach your head; but by the time it reaches your head, your head will have fallen below the horizon.

by Steuard 13y ago

saalweachter 13y ago

This has always bothered me. I am not a point mass. If I can cross the event horizon and not know it, then there is a time when my feet are on one side and my head on the other. If signals cannot cross the event, how would I not notice my missing feet? If signals from my doomed feet can reach my not yet doomed head, then how is it the event horizon?

rca 13y ago
What if the signals emitted from inside the horizon do reach your head, but only once your head have crossed the horizon? Basically, you can change your reference point and consider that the signal is not moving, but your head is still moving towards the signal. This way, you're still seeing your legs. (Note that I have no idea what I'm talking about)
Steuard 13y ago
Well, your feet aren't ever "missing": as far as classical GR is concerned (even with Hawking's semi-classical quantum corrections included), your experience would be perfectly comfortable and unexceptional as you drifted in. The issue is that in that scenario, your head isn't on an escaping trajectory: the nerve signals from your feet might be moving "outward", but your head will be moving inward, and the signal will only get to your brain after your brain has also crossed the horizon. Now, if you were wearing some sort of rocket collar that fired powerfully just before your head crossed the horizon and carried it safely away from the black hole (or even just held it there), you're right: you wouldn't ever receive that signal from your feet. But I'm pretty sure that would be the least of your worries! (And you would notice your missing feet. And torso.) Roughly speaking, the only non-orbital trajectories close to an event horizon that don't fall straight in must be moving pretty close to light speed as seen by infalling observers.
- codeflo 13y ago
  To state that point in another way, the key here is time dilation. (Please correct me if that's wrong.) Let's assume that your feet send a periodic signal to the brain, a "tingling" that let's you know your feet are still there. As your feet approach the event horizon, the tingling will get slower and slower, because time passes much faster for your head than for your feet. As your feet pass the event horizon, the tingling has become infinitely slow (relative to your head). But there's no sharp line where suddenly something happens as your feet touch the event horizon. (All of this of course only in principle and under the premise that you're not smashed to bits at that point.)
  - millstone 13y ago
    I would say this isn't quite right. It's true that time passes more slowly for your feet than your head, but this is due to tidal forces: your head and feet are different distances away from the black hole. For very large black holes, the tidal forces at the event horizon will be small, and the event horizon is the unexceptional, smooth spacetime that Steuard described. So in your example, for a large black hole, you will experience no difference in the rate of tingling as you cross the event horizon. This is what the principle of relativity tells us: you are in free fall, so the laws of physics must appear the same to you.
  - Steuard 13y ago
    I'm not sure that this captures the physics accurately from the perspective that you're describing here. The extreme time dilation that occurs as you approach a black hole's event horizon is really a "global" effect rather than a "local" one: it is defined by the relative difference in how time progresses close to the black hole vs. very far away. When you're falling through the horizon (particularly for a black hole so large that the tidal forces at the horizon aren't deadly), your whole body is "close", so there isn't substantial time dilation between your head and your feet. This is a little bit weird, I know!
  - pdonis 13y ago
    (Please correct me if that's wrong.) It's wrong. Time dilation is not something you observe yourself to experience; it's something another observer observes you to be experiencing. "Time" is relative, so you can feel your own time to be ticking away perfectly normally while it appears to be ticking much more slowly to someone else. As your feet approach the event horizon, the tingling will get slower and slower, because time passes much faster for your head than for your feet. No, this is not correct. As you fall toward and through the horizon, signals travel between your head and your feet just fine, and you don't notice any difference in how fast they travel. But, as I posted upthread, if your foot emits a signal towards your head when it's below the horizon and your head is above it, then by the time the signal reaches your head, your head will have fallen below the horizon.
marcosdumay 13y ago
Thinking about non-ponty masses on General Relativity makes me dizzy (no kidding, I'm quite sure I know the difference between being in a cenrifuge or on the surface of a planet), but you can take for granted that you'll be dead way before reaching the event horizon of a macroscopic black hole.
- codeflo 13y ago
  Is it easier to think about point masses held together by invisible springs? The point masses being atoms, and the springs being electric fields. Not a perfect analogy, but it should work to visualize a lot of the macroscopic effects of gravity. BTW, it's not hard to convince yourself that masses and springs in a centrifuge behave exactly like those near a large body. (In Newtonian mechanics even.) How are you sure you know the difference?
pdonis 13y ago
If signals cannot cross the event, how would I not notice my missing feet? If your feet are below the horizon and your head is above it, then you must be falling through the horizon; it's impossible to remain at a constant altitude at the horizon, even for an instant. So a signal emitted by your foot would still reach your head; but by the time it reaches your head, your head will have fallen below the horizon.