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I Trying to describe my experience crossing an EH

  1. Feb 25, 2017 #1

    Grinkle

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    Any help appreciated. My thought experiment observations are marked with an *.

    I leave my origin and am receiving a continuous beam of photons from my origin. I accelerate to some a speed of (just say) 0.01c. I don't intend any math, but just in case it ends up mattering.

    * As I am accelerating to my travel velocity, I see the wavelength of the origin beacon red shift, and stabilize when my velocity stops increasing.

    I travel for some long time, and my ship is approaching a very large black hole, tidal forces are so small I have no way to detect them or notice them within at least a light year of the event horizon.

    I am still on the origin-side of the event horizon.

    * At some point determined by how precisely I can measure the frequency of the origin beacon, I notice that the frequency is again red-shifting, even though I am not accelerating due to my own ships engine thrust. I am falling into the black hole gravity well.

    * The rate of red shift of my origin beacon is increasing as I get closer to the black hole. I don't feel any different or notice any other macroscopic effects.

    * If I have any other beacons to reference, outlying stars etc, I notice that they are accelerating away from me at a higher rate than my engine thrust accounts for.

    My ship crosses the event horizon.

    * Nothing calls my attention to this.

    * I can reduce the rate of the red-shift, but I will now always only observe an ever increasing red-shift. I can never observe an origin beacon frequency with delta red shift of >=0, no matter how much I accelerate towards the origin beacon with any engine capable of any amount of thrust.

    * Since my engine cannot accelerate my ship at c, my own personal event horizon was much further out than a photon's would be. When I crossed this closer-to-my-origin personal event horizon, nothing special happened, and when I crossed the farther-from-my-origin Schwartz-child EH, nothing special happened. There is no difference in these two horizons relevant to my own human experience. My own personal point-of-no-return determined by my engine power is really the point of most interest to me.
     
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  3. Feb 25, 2017 #2

    mfb

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    There is just a single event horizon. Nothing inside can escape. Everything outside can escape.
    Your limited engine power can make an escape impossible earlier, but that is not a constraint from relativity. Earth does not an event horizon for firework rockets, although they cannot escape.

    Apart from that point, the description looks accurate.
     
  4. Feb 25, 2017 #3

    pervect

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    So far so good. I believe one can attribute the redshift one observe to the tidal forces that you've mentioned are locally negligible. While over short distances they are so small as to not be significant over a short distance. But over the long distance from your source, the effects build up to the point where they can't be ignored. To put it another way, tidal forces can be (more or less) identified with the Riemann curvature tensor, and if said tensor were zero, you wouldn't have any redshift.

    This is probably true, but it's unclear how you are determining the distance. The redshift is something you can actually observe on your instruments, the distance is something that you'd have to compute from your observations. It's not something you'd directly observe, it's part of your mental model.

    So without the details of the model that you are using to create the distance out of the things you can measure (like redhsift), it's hard to make definite statements.

    You're loosing me here. I don't know what you mean by "personal event horizon", or a photon's event horizon. I suspect that you're starting to go off-track here. Do you have a reference, or is this something you concluded on your own? I'm suspecting the later.

    Still lost. "Personal event horizon"? Where did you read about this (if you did read about it). How did this idea ome about, and was it from something that was published?
     
  5. Feb 25, 2017 #4

    phinds

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    It seems clear to me that he has simply extended the concept of "horizon" as follows: there is an EH which defines the place where light can no longer escape from the BH's gravity well. My engine has a certain amount of power and there is some point at which that power will no longer be sufficient to allow me to escape from the gravity well. I'm going to arbitrarily call that my "personal horizon". It's not an unreasonable definition, it just isn't something that is particularly useful and is totally dependent on his particular engine, not any special underlying science.
     
  6. Feb 25, 2017 #5

    Grinkle

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    @phinds Yes, that is what I meant.

    My thinking here is that all of my observations and experiences can be described purely with classical physics. Crossing the EH as defined in relativity is as noticeable to me on this journey as seeing a sign on the road saying "Welcome to Arizona", when 50 miles previous I didn't have enough gas left to turn around and refill anywhere except ahead of me anyway.

    ;-) As an engineer, I think its a hypothetically more useful thing to know than where an actual event horizon is to a traveler who would be interested in a return trip.

    A question -

    After I cross my own point of no return, what I see is that my engine thrust cannot cause my origin beacon to stop its increasing rate of red shifting.

    Are there any other observations I can make in between this point and the actual event horizon that would be different than the observations I make immediately after crossing the event horizon?
     
  7. Feb 26, 2017 #6

    PAllen

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    This is not true. Even inside the event horizon, while looking at at an outside beacon (e.g. star), by firing your rockets sufficiently in the appropriate direction, you can see the star arbitrarily blue shifted. At any event inside the horizon, you still have a local Lorentz frame. This means, that for a given incoming light signal, all available doppler shifts are available for different local velocities. Irrespective of this, firing your rocket will not slow your reaching the singularity.
     
  8. Feb 26, 2017 #7

    Grinkle

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    Perhaps the problem is again me not understanding how to think about reference frames. In a reference frame where I am freely moving with the beacon (eg just prior to my departure), I record a baseline frequency. Inside the EH, if I ever see the beacon frequency blue-shifted with respect to this baseline, I think that implies that I am expecting to be able to reach the beacon in finite time from my current reference frame. I think I should never be able to conclude that I can reach any beacon in finite time that is outside of the EH.

    Where am I going wrong?
     
  9. Feb 26, 2017 #8

    A.T.

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    Man... when I read the title, I thought you actually did it.
     
  10. Feb 26, 2017 #9

    PAllen

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    SR must be true locally, always and everywhere, per the mathematical structure of GR (this is one universally correct formulation of the POE). If one observer sees a light signal at one frequency, then another collocated observer at some relative relative velocity to the first will measure a frequency determined by SR Doppler formula. All relative velocities are locally available everywhere - again this is the POE.
     
    Last edited: Feb 26, 2017
  11. Feb 26, 2017 #10

    Grinkle

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    Is there something wrong or missing with the following? I am stuck with a contradiction.

    1. If I see a blue shift, it means I am getting closer to the source.
    2. I will calculate some finite time to reach the source assuming I am always able to maintain a blue shift.
    3. Since all relative velocities are locally available to me, I can maintain a blue shift.
    4. I can never again cross the EH, and the source will never come to my side of the EH, so I can never actually reach the source, even after the amount of time that I calculated has passed in my own current inside-the-EH frame.
     
  12. Feb 26, 2017 #11

    Ibix

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    You forgot about the gravitational blue shift.
     
  13. Feb 26, 2017 #12

    Dale

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    Hmm, is this true? There is redshift due to relative velocity, but also blueshift due to being deeper in the gravity well. I am not sure which wins out. It is probably best to not try to separate out the velocity and gravity shifts in this case, but I don't have a good intuition about it.
     
  14. Feb 26, 2017 #13

    PAllen

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    1) Not true in GR at all. There is no global notion of distance at all, so relating spectral shifts to distance change has no invariant meaning. On the other hand, spectral shifts themselves are invariant.
    2) Also untrue in general in GR. You can have blue shift while receding from a source per some reasonable chosen distance convention ( but see above about severe limitations on notions of distance in GR).
     
  15. Feb 26, 2017 #14

    PAllen

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    If you start free fall from infinity, distant stars will be moderately red shifted at horizon crossing. If you start free fall from hovering close the horizon, stars can be arbitrarily blue shifted at crossing, the closer to the horizon your starting point is.
     
  16. Feb 26, 2017 #15

    Dale

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    Interesting. Then there should be some critical radius at which you are neither red nor blue shifted at the horizon.
     
  17. Feb 26, 2017 #16

    pervect

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    I suppose this makes sense. If you hover over the horizon, you can get an arbitrary blue-shift by getting close to the horizon. If you are momentarily stationary, you get the same blueshift at that instant in time as you would if you were hovering, though it doesn't last long, so you won't (for instance) see the entire future of the universe, as you might if you hovered close enough.

    And I recall from previously working it out that there is a 2:1 red shift free-falling from infinity.
     
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