Falling into a black hole. Where am I wrong?

1. Imprecise, but OK

2. Be careful about your use of the word "notice," which has no specific operational definition.

3. You incorrectly describe the light from the rest of the universe as taking up a very thin disk behind you. That would be true if you were remaining stationary above the hole, but to a falling observer, less than half the sky is taken up by the hole.

4. You are misleading yourself by discussing how much time on your watch equals how much time on someone else's without specifying a reference frame. The rate of an exterior clock as measured by you as you fall inwards is not as fast as you seem to think, nor is it asymptotic. What you are describing (exterior clocks getting asymptitically fast as you approach the horizon) is true when you consider a sequence of stationary observers standing on platforms above the hole, but is untrue for someone actually moving towards the hole. The falling observer observes much less rapid progression of distant clocks.

The same is also true for your description of the sky, which is true for a sequence of stationary observers hovering above the hole, but not true for the falling observer. At just above the event horizon, a stationary observer, but not a falling observer, observes all the light from the universe arriving from the zenith. A falling observer observes a disk of the sky of only about 42 degrees radius to be taken up by the black hole, and the light from the universe takes up the rest. In fact, to that observer, even after crossing the event horizon, the black hole never ever takes up more than half the sky.

The same is true for the blueshifting. Only the stationary observer observes the light to be asymptotically blueshifted. The falling observer disagrees.

5. Incorrect. You do not measure exterior clocks to tick asymptotically fast. You do not observe an infinite amount of time passing in the external universe. That is only observed by a stationary observer hovering just outside the hole, not the falling observer. You do not observe very much time to pass on external clocks at all, and you certainly don't see all the other BHs evaporate, much less yours.

6. Yes you can, and you do.

7. Therefore, no.

You are taking some description you are reading of what life is like for hovering observers around a black hole and attempting to apply this to an infalling observer, who is moving at nearly c relative to them. Obviously that will not work. One way to think about it is that the time dilation from the nearly-c motion of the exterior universe nearly cancels the gravitational blueshifting you are talking about.

You do see the universe behind you speed up, but this does not continue to infinity. When you reach a point sufficiently close to the existing event horizon such that your mass, added to the mass of the black hole, would put a new event horizon further out that you are, then that new event horizon does form, and you are inside the black hole.

Lola F's answer is the best so far. I had been confusing the "shell" (hovering) reference frame with the "raindrop" (falling) reference frame. One must combine the effect of special relativity to that of the gravitational relativity to see what really happens. Read the Wikipedia article on Gullstrand-Painlevé coordinates.

http://en.wikipedia.org/wiki/Gullstrand%E2%80%93Pa...

Due to gravitational time dilation, to the outside observers you will appear to slow down as you reach the Event Horizon. From the perspective of the observer, you will eventually appear frozen in time.

However, that does not save you from your ultimate fate.

While you may seem frozen in time to the outside observer, you are in fact still falling into the Black Hole and eventually all the matter that once made up you, will find its way to the singularity where it will be crushed to infinite density and zero volume.

The time it takes for you to fall into a Black Hole is finite, the time it takes for the final photon of light to get back to the Observer that shows you actually crossing the Event Horizon is infinite.

Don't confuse what someone sees with what someone can calculate.

For example, someone can calculate that you have fallen into a black hole even though you image continues to appear on the event horizon (getting redder and redder and smaller and smaller all the time). Just because your image remains (which is caused by the time that it takes light to escape when near the event horizon), does not mean that you remain outside the event horizon.

Also remember that it is SPACE that is slipping into the black hole and it is dragging both you and light into the black hole. It does not slow down as you get closer, it speeds up. The space dragging is also why you can cross the event horizon and not die for at least a little while.

To an outside observer, your speed at the event horizon is the speed of light. But in your reference frame it is not. This is because it is space slipping into the black hole.

Dump has a great reference site (read it!),

But, you and most of the others make a mistake regarding the outside world. If you are falling into a black hole, the outside world red shifts and slows down, not speeds up. The outside world will be receding at a faster and faster velocity as measured by you. If you want to, you can count the arriving wavelengths of light emitted from the outside world to learn the truth. Or imagine that you traveling with the raindrops falling into the black hole. The closer they get to the event horizon, the faster the outside world is receding.

It is only if you stop your decent ("hover") that you see the outside world blue shift. And a bright blue world it would be. Now you are looking at a gravitational blue shift.

So here are your answers:

1. Yep

2., 3, 4 Nope, your increase in velocity means that the clocks behind you will now start to red shift and slow down. They, too, would notice your clock slowing down. However, their slowing down is solely due to the red shift caused by your acceleration. You would be more red shifted to them, then they are to you (i.e., you would be going slower).

However, clocks that are in front of you -- say a star system behind the black hole, but visible to you -- would blue shift and appear to you to speed up.

5. Nope. The outside world will calculate that you fell into the black hole quite quickly, but your image is still seen on the event horizon getting redder and redder and smaller and smaller

6. Nope

7. Nope.

*****Addendum *********

I did a quick read on the original paper that was a basis for the science-news blog you cite. Here it is: http://arxiv.org/pdf/gr-qc/0609024v3

Interesting -- but even if true, don't assume that lack of information loss is a preservative to immortality by living on the event horizon of a black hole forever. It would take as much energy to recover that information as the black hole gained in mass by swallowing you.

(If I have the time and energy, I might give it a thorough reading.)

Aside from your silly assertion that tidal and radiation forces aren't a problem?

Tell me again, what do YOU experience as you accelerate into the black hole? Ignore your observations of the "blue spot", what happens to YOU? Remember your clock is ticking away "normally", you are accelerating into the BH, through the EH.

<edit>

I normally get a little perturbed when I post a correct answer and get (two!) thumbs down. But pearls before swine...

I guess its not like anybody can prove me right or wrong concretely, so I'll refrain from challenging them. Anyway,

Lets say you're at a distance of 100,000 from the EH and traveling at a speed (relative to the BH) of ½c. Exactly how many heartbeats do you have left before you hit the event horizon (EH) and oh by the way the tidal effects disintegrate your pieces parts?

I like Lola's ans too.

and by "hit" I mean reach and continue on in towards the center singularity → chasing rainbows...

And how do you see YOUR OWN clock slow down? You don't. Starting some distance from the event horizon, you will cross it in a finite time.

I do not know in any detail Lawrence Krauss' and his Case Western Reserve colleagues' work but what it may mean could conceivably not be accurately reported.

I think you're OK through step #4, but in step #5 "your" black hole remains intact because it is within your frame of reference. You can't make sense of the situation by switching back and forth in your mind between frames of reference and trying to reconcile them. They aren't reconcilable. You fall right on through the event horizon and notice nothing unusual about the journey.

1. Yep

2. Yes.

3. You should see other clocks at the same rate as normal, only yours will appear to them to slow down as you approach the event horizon. Oh and the outer universe will look completely normal to you.

4. This is where you're going off track. Your watch continues at the moral rate, you don't slow down at all, only the light coming off you is having trouble getting back to observers, that's why you appear to slow down, though in reality you haven't - if anything you'll have sped up.

5. No, you went through straight away. There would only be a frozen image, gradually fading to IR and lower frequencies.

6. No, you got crushed long ago.

7. As I've said, things don't slow down approaching a black hole, they only seem to because of the blackhole's effect on the light coming off them.

Having said this I don't think black holes exist, as its based too much on outdated classical mechanics (like the concept of a singularity itself) and not quantum theory. I personally think that there is merit to the theory of gravastars which I suggest you investigate. You might also be interested in dark energy stars and fuzzballs.

I've read in the Bible about people using great swelling words of vanity and who by taking thought can add one cubit to their stature? james the hollow earth man

Wow that's a good question.