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Black hole questions

  1. Oct 31, 2006 #1
    1. From our frame of reference, it takes infinite time for an object to pass the event horizon of a black hole. Does that mean there simply isn't enough time for any black hole to form in the first place?

    2. When an object of mass m falls into a black hole of mass M, the mass of the black hole will become M+m, right?

    My problem is that the object's mass increases with its speed and approaches infinity near the event horizon. Theoretically its mass can exceed M+m just before it reaches the event horizon, right? To me, that doesn't add up.

    Thanks in advance!

    Wai Wong
     
  2. jcsd
  3. Oct 31, 2006 #2

    TDS

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    A Laymans answers.

    Wai,

    I hope that you do not mind a Layman's answers to your questions.

    1) From our frame of reference the observer should see the object enter the Accresion Disk in a time relative to the observer. Example, an observer sees an object approach the accresion disk at a velocity the would put the object in the accresion disk in a weeks time of being observed. Once the object is trapped in the accresion disk, it now moves at the velocity of the rotation of the disk. At that velocity it may take a year for the object to enter the Event Horizon. The time that it takes for the Star to become a Black Hole would be based on the size of the star and the age of the star. The two situations are not related. In my humble opinion anyway.

    2) Logically you are correct. Anytime you add something to something its mass should increase. But I bet that someone here will probably find a way to negate this.:rofl:

    I hope that I have been able to help.

    TDS



     
  4. Oct 31, 2006 #3
    I think that is not correct. If the object falling into the event horizon is a clock, it will appear to be running slower and slower and almost coming to a standstill just before entering the event horizon. To us, whenever we look at it, we can always see the clock just above the event horizon. Of course, that is purely theoretical, because the photons emitted from the clock would have red-shifted to undetectable energy levels.

    Wai Wong
     
  5. Oct 31, 2006 #4

    pervect

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    Simultaneity is relative. From the point of view of an observer falling into a black hole, there is no problem regarding its existence.

    The analogy between the event horizon of a black hole and the so-called Rindler horizon of an accelerating observer helps illustrate the difficulty with the viewpoint that a black hole "doesn't exist" or is a "frozen star". The "frozen star" view used to be quite common, but has more or less faded away. Of course, this is really a philosophical question in disguise, because it is concerned with "existence".

    Here's the scoop on the Rindler horizon. If you get into a rocketship, and accelerate at 1 gravity, you can, given a headstart, outrun light. Greg Egan talks a little bit about this at http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html

    You never exceed the speed of light, but you always stay just a bit ahead of a light beam. As a consequence of this fact, there is an event horizon behind you, which is mathematically quite similar to the event horizon of a black hole. If you think in non-inertial frames, you can say that this event horizon is due to the uniform gravitational field cuased by your acceleration.

    Now, suppose you are on such a space-ship. If you keep accelerating constantly, from the POV of the space-ship the Earth never gets beyond a certain critical point, for instance at 1g the Earth never gets much older than 1 year old. So the Earth "freezes" from the POV of the space-ship, and never crosses the horizon. Of course, there is absolutely no problem from the POV of the Earth. Nothing specially happens at 1 year. The problem is entirely with the POV of the spaceship. This suggests caution in adopting the "frozen star" viewpoint, it doesn't always give an accurate picture for all observers. The key point is that the time to fall-in is infinite in the coordinate system of an outside observer, but finite for the coordinate system of an infalling observer.

    Onto the second question. The mass of a Schwarzschild black hole increases not by the mass of an object that you drop into it, but by the energy-at-infinity/c^2. (Energy at infinty is the term used by Misner, THorne, Wheeler in "Gravitation"). A more sophisticated way of saying this is that the ADM mass of the black hole and the infalling object is a conserved quantity.

    So if you have an object that is motionless at infinity, and let it drop into the black hole, the black hole increases by the mass of that object. If you have an object that is moving rapidly at infinty, the mass of the black hole increases by more than the mass of a black hole. If you have an object that does not have enough energy to espcae to infinity, the mass of the black hole increases by LESS than the mass of the object. It is the energy-at-infinty that is conserved. The conservation of the energy-at-infinty is due to the fact that the Schwarzschild space-time is static. (The ADM formulation of this conservation law relies on the fact that space-time is asymptotically flat, rather than the fact that it's static. The Schwarzschild space-time is both. The ADM formulation is needed if the infalling object is significant compared to the mass of the black hole, as the resulting space-time is no longer Schwarzschild nor static. However, the "energy-at-infinty" formulation is much more tractable mathematically and is the one given in most introductory textbooks.

    See the thread on energy conservation in GR for more on that topic.
     
  6. Oct 31, 2006 #5
    I have no problem about the existence of black holes from the infalling object's POV. My point is, we can never feel the effects of black holes. What we can feel is the effects of stars or other matter 'about' to become black holes, unless we are unlucky to cross the event horizon ourselves. In other words, any attempt to explain any phenomenon using black holes must be flawed because the effects of black holes have not reached us yet. One can only say a certain phenomenon is caused by a dying star about to become a black hole.

    My problem is that the object's relativistic mass itself exceeds the total mass when it approaches the event horizon. Thus mass cannot be conserved. Such an anomaly can be avoided if my assertion above is correct, i.e. such anomaly has not happened yet.

    Wai Wong
     
  7. Nov 1, 2006 #6
    On second thought, I do have problem about the infalling object's POV. My question is: can the infalling object feel the gravity of the BH? It seems to me that the answer should be no, because light just above the horizon has not reached the object, and gravity cannot travel faster than light! Instead, it should be feeling the gravity of the BF forming matter before the BH is formed.

    From the object's POV, it should always see a lot of matter above the event horizon about to enter the BH. The closer it gets to the event horizon, the more photons will hit it. Before it can cross the event horizon, it will be disintegrated by the radiation and extreme temperature.

    I am likely to be wrong, but can anyone enlighten me?

    Wai Wong
     
  8. Nov 1, 2006 #7
    By Einstein's equivalence principle a free falling point mass never feels the influence of gravity.
    However since the gravitational field of a black hole is not uniform there are tidal effects, so if the object is of any significant size it would deform.
     
  9. Nov 2, 2006 #8
    I agree that the object will experience tidal effects, but the gravity it experiences does not come from the black hole, it was released from the raw materials that formed the black hole *before* they cross the event horizon.

    As a thought experiment, suppose a black hole was formed 10 billion years ago and a clock set at 0:00 was dropped 1m above the event horizon into the black hole. When we observe the clock now, we can still see a very thin clock at time 0.0...01s about to cross the event horizon. It is time dilation that turn this 0.0...01s into our time of 10 billion years. 20 billion years from now, our descendants can still see the clock, just a tiny bit closer to the event horizon. In other words, it takes 20 billion years for light to travel that tiny distance. Since gravity has the same speed as light, it takes gravity the same 20 billion years to travel that tiny distance. As the black hole is only 10 billion years old, its gravity has not traversed even that tiny distance! The gravity that reaches us come from objects that were outside the event horizon like the clock.

    Again, my assertion is that we can never feel the effect of black holes.

    Wai Wong
     
  10. Nov 2, 2006 #9
    Actually you are mistaken.
    You thought experiment assumes that the mass making up the black hole was created instantly. Instead it was simply caused by the accumulation of enough mass and an insufficient resistance from EM and other forces to counter the gravitational collapse. Each time an additional mass object joined the sphere it adjusted the spacetime curvature was adjusted.

    Think of the whole spacetime manifold of the universe, every particle's shape of the worldline is subject to the local curvature of spacetime. But at the same time each particle with mass or anything with energy will change the curvature of spacetime.
    Now in GR there is no action at a distance. An object removed far away from a black hole starts to move in the direction of the black hole because the local curvature guides it not because there is some information on the distant mass density.
     
  11. Nov 2, 2006 #10
    That comes from a bad choice of coordinates. The object goes through the horizon in finite proper time. If you want to describe the event using Schw. coordinate time, you'll find that the object goes through infinite coordinate time in order to reach the event horizon, and then goes back through (coordinate) time until reaching the interior in a net coordinate time that is not too different from the proper time.
    Sure.
    Mass doesn't increase, really. We've tried to get that interpretation out of relativity for some time now.
     
    Last edited: Nov 2, 2006
  12. Nov 2, 2006 #11

    pervect

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    See for instance
    http://casa.colorado.edu/~ajsh/collapse.html#collapse

    http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html
    I believe this question is also addressed in Kip Thorne's book (Black Holes: Einstein's outgrageous legacy) but my copy has wandered off again.

    Note that the question of how the gravity gets out of the black hole has also been addressed in the above two web pages, though there is perhaps slightly less agreement about how to explain the answer. But the answer is very clear - gravity does get out of a black hole, and so does the columb force due to the black hole's charge.

    You might also want to look at
    How does the gravity get out of a black hole?
    Does gravity travel at the speed of light?
     
  13. Nov 2, 2006 #12
    Thanks for your reply!

    Pardon me for still using the cordinate time. If the object can go back through coordinate time, does that mean it can exist in two places (one outside and one inside the event horizon) at the same coordinate time? If so, can we feel the gravity of the object (and all other stuff) inside the event horizon?

    How about energy? At some point before the event horizon, the kinetic energy of that object will exceed (m+M)c^2, which is impossible. So, the object can never reach that point, but yet it can somehow 'tunnel' through that barrier into the black hole!? Is it possible to calculate the coordinate time when such tunnelling occurs?

    Wai Wong
     
  14. Nov 2, 2006 #13

    pervect

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    You are using SR formulas here where you need to be using GR formulas. The correct formula for the "energy at infinity" of an infalling object is a constant. You can find the correct formulas in several textooks, or online at http://www.fourmilab.ch/gravitation/orbits/ where the 'energy at infinity' is called ~E.

    Furhtermore, when the infalling object crosses the event horizon, what gets added to the black hole's mass is the "energy at infinity" / c^2, assuming that the infalling object has a negligible mass compared to that of the black hole so that the momentum of the black hole is essentially unchanged. The mass of the infalling object does not get added - what adds is the energies. For instance, an object of rest mass m, suspended just above the event horizon, and dropped in will not contribute appreciably to the mass of the black hole, because its "energy at infinity" will be essentially zero.
     
    Last edited: Nov 2, 2006
  15. Nov 2, 2006 #14
    Yeah the event horizon does increase in finite coordinate time so yes you will need more than one worldline with these coordinates. But we're fine so long as the particle is out of reach by the time you register the increase. IE even a photon can't catch up to it now ("before it crosses over"). See this is just strange coordinates.
     
  16. Nov 2, 2006 #15
    I did not assume the black hole was formed instantly. I just assume the black hole was there when the clock was dropped 10 billion years ago. To me and my descendants, the clock is always outside the event horizon. In other words, nothing has ever joined the sphere. Regardless of when the black hole was formed, its gravity has not travesed the tiny distance that the clock takes 20 billion years to traversed.

    My point is there is curvature of spacetime around a 'black hole', but that curvature is caused by the black hole's building materials before they cross the event horizon. You can't count the gravity of the materials twice. You can only ignore the infalling materials' gravity only if they have crossed the event horizon.

    Wai Wong
     
  17. Nov 2, 2006 #16
    I realize that, but that is the whole problem with your thought experiment. :smile:

    Correct.

    Here you are obviously wrong. It actually happened, it did pass the event horizon but you simply cannot detect it from your frame of reference.

    Again you are assuming that because you do not see it going past the event horizon that it did not happen. It did happen, but you simply cannot detect it.

    A black hole's event horizon is not the only type of event horizon in relativity. For instance, two objects that are accelerating away from each other with a given initial distance cannot see each other's light signals either. Would you by analogy conclude that nothing is happening at the other location or perhaps even that it does not exists?
     
  18. Nov 2, 2006 #17
    Thanks to the responses from you experts, but I am unable to comprehend most of your arguments and links, except for those based on frozen star theory which I agree.

    Let me perform a final thought experiment. Suppose I dive into a nearby black hole today wearing a mirror on my back. A billion years from now, someone, say Alice, on earth sends me a flash of light. My questions are:

    a. Will I receive the flash before I cross the event horizon? I think so.
    b. Will the flash be blueshifted or redshifted? I think it is extremely blueshifted.
    c. Will the reflection of the flash be received by earthlings some time later? I think the reflection will be received several billion years from now somewhat redshifted.
    d. If the flash contains information (e.g. Morse code representation of Alice), is the information intact in the reflection? I think so.
    e. If I decide to return after receiving the flash, will it be too late? I don't think so. I think I can return to the earth to meet Alice's descendants.

    Am I correct? If so, then the frozen star scenario is not an optical illusion - I can still send information 1 billion earth years after I dive in, and Alice's persuasion can rescue me from falling into a black hole 1 billion years after I dive!

    Wai Wong
     
  19. Nov 2, 2006 #18

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    You will not receive the flash of light before you cross the event horizon. This is mentioned in several of the FAQ's I've been quoting.

    For example http://casa.colorado.edu/~ajsh/singularity.html

    and also http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

    If you have the math, you can work this out from a standard Finklestein diagram. I'm sorry if you don't have the background to understand the arguments, I'm not quite sure what to do about that. I could probably dig up some textbook references in addition to the online web references I've been quoting, but I suspect that's not the issue here.

    Have you actually been reading any of the web references I've been posting on this fascinating subject, or have you just been making stuff up out of your own imagination? I get the unfortunate impression you've been mostly "making stuff up" rather than doing any serious reading (including the popular references I've quoted which should be accessible enough to show you, at a minimum, that your ideas are not correct, even if you don't have the math at the current time to go into more details.)

    I've worked out what happens in the specific case of someone free-falling into a black hole from infinity (i.e. zero energy at infinity) and viewing a radial light beam from behind him. The light that that particular observer sees is redshifted by a factor of 2:1 when he is at the event horizon. Detailed calculations are required, because gravity blue-shifts the light, while the doppler effect redshifts the light. Another poster here has confirmed that answer. The general answer will depend on one's exact trajectory - one can see the distant light either redshifted or blueshifted, depending on the exact details. The red or blueshift will also depend on the angle, the case I worked out was the simple case where one looks directly astern.

    http://casa.colorado.edu/~ajsh/, which has some movies of what someone would see falling into a Schwarzschild black hole, also talks a bit about this in more detail (redshift/blueshift vs angle).

    many of the remainig points and questions are somewhat irrelevant given the above.
     
  20. Nov 3, 2006 #19
    As far as I understand, the two events - the clock crossing the event horizon, and we see the frozen clock now - are spacelike. So I don't understand why you use past tense for the former event. I think the order of such event pair depends on which observer you are talking about. For us, the former event should be in the future.

    When did it happen? According to the clock's proper time, it takes a finite time (say 1ns) for it to reach the event horizon. Does that mean the clock crossed the event horizon 10 billions years minus 1ns ago? Of course not. The 1ns dilates to infinity in our coordinate time.

    Firstly the situation is different because there is no time dilation caused by gravity.

    Secondly, if the objects are allowed to stop acceleration, they can find out if the other object exists. But if there is a physical law that prohibit them from accelerating, and no third observer can be present, then the answer to your question is purely philosophical. Hypotheses that say there are 0, 1 or 2 objects at the other end are equally unprovable.

    According to the following http://casa.colorado.edu/~ajsh/collapse.html:

    Gravity does not escape from a black hole. Gravity moves at the speed of light, and cannot get from inside the horizon to the outside world. The gravity felt by a person outside a black hole is the gravity of the stuff that fell long ago into the black hole.

    So whether the black hole is formed in the past or in the future makes no practical difference.

    On the other hand, if one uses a black hole for any calcuation, the result is just an approximation of the remnant effect of the collapsing star.

    Wai Wong
     
  21. Nov 3, 2006 #20
    Both links say I won't see the future and that is what I couldn't comprehend. My rationale was: I am catching up with future, so whatever future event it is, it is a past event to me before I cross the event horizon. So their use of the term 'future' didn't make sense to me. Of course I was mistaken. From the POV of Alice, although I am not yet cross the horizon, her flash cannot catch up with me because I am accelerating away. From my POV Alice is still future when I cross the event horizon.

    But that doesn't mean I can't see future events like Alice's flash. Before I reach the singularity, I might see her flash. See

    http://www.engr.mun.ca/~ggeorge/astron/blackholes.html

    The fall through the event horizon is survivable, but the fall through the Cauchy horizon is not. All the light which will ever fall on the black hole in the entire future of the Universe will catch up with the observer before he crosses the Cauchy horizon. Looking up out of the hole he will view the entire, possibly infinitely long, history of the Universe from light whose blueshift and energy increase without limit, all in a matter of seconds. The energy falling on the observer at the instant of crossing the Cauchy horizon will be infinite.

    That is somewhat like what I envisaged in my thought experiment but is contrary to either of the above links. To me, what is perceived beyond the event horizon is anybody's guess, because no one knows how our senses work when time and space swap, and even whether GR works there.

    Imagine teaching a child about the concept of negative numbers. He will always come up with questions, some silly, some sensible before he grasps it. The way to teach him is by answering his questions and give analogies. That is why I asked here. Luckily I got it (I think) after your answers to my final thought experiment. I am really grateful for your help, honestly. I must also acknowledge other experts' responses are helpful and appreciated.

     
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