Tuesday, November 18, 2014

Black holes: the Faller's Perspective

Over the last 20 years I've read a number of popular physics and even some physics texts on this subject.  As I write this entry I am not referring back to those texts but instead attempting to summarize what I remember as well as apply what I know of the physics to the problem.  So my ponders might veer radically away from accepted interpretations of what this might look like :)

Having recently watched the movie Interstellar (twice), my thoughts turned to their treatment of black holes.  Since the movie is ultimately a story about relationships, they threw out the inconvenient pieces of science and replaced them with more palatable fictions - an artful weaving of science and fiction, IMO.

In my last entry, I wrote what I felt the outside observer would see as something/one fell into a black hole.  This is my attempt to describe what the faller might observe as he fell into the black hole.

By the way, despite numerous science and engineering holes and gaffs, I loved the movie.  If you enjoy reading this sort of blog post, then you'll love the movie too.

Interstellar


Image from Wired

The Four dimensional perspective

and by four dimensions, I mean time as well as the three spatial dimensions.

Time

The faller does not sense time stretching or slowing in any personal way.  But he can detect deviations in his time perspective from that of the outside universe by looking up and observing the Universe.

As mentioned in my previous article on this, as the faller approaches the event horizon his time dilation diverges more and more from the outside observer's frame.  *Before* he reaches the event horizon, his time slows in comparison to the outside universe's time by enough that the Universe evolves before his eyes and eventually goes dark (the mechanism by which it goes dark depends upon the amount of dark energy acceleration).

The time dilation is an interesting problem because we must account for both the time dilation of traveling close to the speed of light AND for the proximity the mass of the black hole.  I haven't worked out the combined effect but I might do that when I get a chance.

The normal thinking about what happens to a falling observer is that he passes through the event horizon and no observation would tell him that he's passed the "point of no return."  But if my prior article is correct and his t -> 0 (compared to the outside universe), then something magical will happen.

Unfortunately for you, you'll have to read through the next two sections before I get to the magic.

Space

In the previous article, I mentioned that to an outside observer all of the mass attempting to flow into the black hole, instead accumulates in a shell outside the event horizon.  The observer falling into the black hole does NOT see this.  The objects falling in front of him always remain in front of him while those following him continue to follow him and they retain their original shape (and don't get squashed onto the sphere of matter traffic jammed trying to get through the singularity).

In the simplified sense, the falling observer can get a sense of his progress towards the black hole simply by watching the angular diameter of the black hole.  This angular diameter represents a cone of observation and when the angle of that cone = 90 degrees, the falling observers has fallen through (the details of this will make it so the angle will be some small value above 90 degrees but I don't want to do the math - this exercise is left for the enjoyment of the reader, lol).

The falling observer could track his progress after passing through the event horizon by monitoring the shape of cone.  Just prior to reaching the singularity, the number of light paths which could still reach the observer would collapse until just a straight line from the singularity through the observer out to the universe would remain to allow light to reach the observer.

Other stuff

Gravity (always messing things up)

I *think* my simplified case is too simplified and that the observer could not rely on the angular diameter of the black holes blackness to determine progress - possible for all cases but certainly for cases past the event horizon (the falling observer would certainly be able to calculate when/if he passed through the event horizon).  This is because the gravity in this region is so powerful, that it'll warp the light around.  Perhaps what the observer would see would look like a giant fish eye lens of the entire universe.  While the falling observer could still never see beyond his contracting local frame of reference below him, he will be able to see the rest of the Universe.

Hawking Radiation

Reputedly, nothing radiates from black holes.  Yet Stephen Hawking proved (I think in the 1980s) that black holes DO radiate (black hole radiation temperature is inversely proportional to the square of their mass).  When something radiates, it loses energy.

E = m * c^2

A black hole losing energy is therefore also losing mass.  Meaning all black holes eventually "evaporate" if given enough time.  The rate of mass loss would be measurable (in theory) to the outside observer - meaning the black hole would possess a finite life to the outside observer.

Magic

The outside observer sees the faller progress towards the event horizon and when the faller gets really close, he appears to smear out into the sphere surrounding the event horizon - literally never falling through.

The falling observer sees himself accelerate towards the event horizon and as he gets really close, the time of the Universe accelerates into over drive and Universe and everything in it evolves before his very eyes (billions, trillions, or more years passing - depending upon the black holes mass).  As the falling observer got close to the event horizon, the black hole would begin to shrink (due to Hawking Radiation evaporating it).  Just before he got to the event horizon the black hole will have completely evaporated.


Bad stuff
At least if you're the falling observer...

What happens to the rest of the shell of matter surrounding the event horizon when the black hole evaporates?  I'm not entirely sure, but I suspect that since each bit got caught in the time dilation fly paper at different times, each bit of matter gets unstuck at different times too.

Since all the mass in the shell around the event horizon constitutes part of the mass of the black hole to observers far away from the black hole.  This means the evaporation of the black hole includes the evaporation of the mass shell around the event horizon.  Which sounds like what I said above - bits of matter in the shell evaporate and fly off over time.

I don't know about you, but evaporating the observer doesn't sound very healthy for him.

This actually ties in with the interpretation of a fiery thermodynamic hell surrounding the event horizon as envisioned by some.

If this interpretation is correct, then the falling observer will also suffer from increasing temperature as he falls towards the event horizon.  Assuming he could survive the environment (he couldn't), he would observe the "magic" identified above.  The reality is he would be torn apart, evaporate, turned to plasma, scattered, and then individual particles would evaporate from the black hole by "Hawking Radiation".

Previous related entry was Black holes: Initial thoughts

Next related entry

2 comments:

  1. "his time slows in comparison to the outside universe's time by enough that the Universe evolves before his eyes and eventually goes dark (the mechanism by which it goes dark depends upon the amount of dark energy acceleration)." This is actually a misconception, see the "Will you see the universe end?" section of http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html along with http://physics.stackexchange.com/questions/82678/does-someone-falling-into-a-black-hole-see-the-end-of-the-universe and "answer to quiz question 5" at http://casa.colorado.edu/~ajsh/singularity.html

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    1. I read through the stack exchange answer. The proof only shows that the observer passes through the event horizon in finite time - which my entry agrees with.

      I have been wondering about the effects of coordinate selection for relativity. It appears that this concern was appropriate and the solution I derived from my coordinates is probably not correct.

      Now I'm still thinking we can't provide a positive solution until we develop quantum gravity.

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