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What is inside a black hole?

  1. May 20, 2013 #1
    I have a basic question.
    It is well known that according to "our" time (time measured by an observer in flat space-time), an object falling into a black hole will never cross the event horizon (though, of course, according to its "proper time" it will fall into the singularity in a finite time) on account of time dilation near the black hole.
    So, can we say that since the beginning of the universe, nothing has ever crossed over inside any black hole in "our" time. All events beyond the event horizon are in the future of "our" time, which may be infinite?
    Comments/corrections are most welcome.
     
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  3. May 20, 2013 #2

    phinds

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    "Our" time is an optical illusion and not meaningful in terms of what happens locally. I think you already get this, so what's your point?
     
  4. May 20, 2013 #3

    Simon Bridge

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    Welcome to PF;
    I managed to tie myself in knots in this one too ...

    I think there are a lot of misunderstandings evident in what you wrote - but I'll just go right to the nub of your question and maybe tackle these later (or someone else will).

    By "inside" you mean, "within the radius of the event horizon"?
    You want to know what happens as an object approaches a black hole from the point of view of an observer far from the hole, but stationary wrt the hole's center of mass?

    It's tricky.

    Oversimplifying: the effect is that the event horizon expands to enclose an object that approaches close enough. Recall that the radius of the event horizon depends on the mass inside. So something need only get close enough to within where the new event horizon is going to be to get "caught".

    Now I just know that some people are going to take great exception to this description (I know I'm wincing a bit) :D
    I'd love to see a better way of describing it myself so, like you, I wait.

    [edit] had a look for the place I got this impression from and cannot find it quickly ... suspect I got something horribly wrong <braces self>
     
    Last edited: May 20, 2013
  5. May 20, 2013 #4

    WannabeNewton

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    Coordinate time is a physically meaningless quantity. When speaking of elapsed times between events the only meaningful quantity is the proper time and for this there is only a finite amount needed for the in-falling observer to cross the event horizon. Phinds has already noted this above. You can make a judicious choice of coordinates and eliminate the coordinate singularity at the event horizon.
     
  6. May 21, 2013 #5
    "Our" time is an optical illusion and not meaningful in terms of what happens locally

    I agree that in terms of what happens locally, "our time" is an illsion. But, at the same time, it is more or less (neglecting local motions of earth, sun, Galaxy and local galactic supercluster etc.) it is the cosmic time depending only on the scaler factor. It is the only absolute time that can be measured anywhere in the universe. Moroever, it is the time that we perceive. Proper time is not "our" time unless we are falling into the black hole, in which case what we perceive or experience is unlikely to be available to the media.

    ...so what's your point?

    My point is precisely this:
    So, can we say that since the beginning of the universe, nothing has ever crossed over inside any black hole in "our" time. All events beyond the event horizon are in the future of "our" time, which may be infinite?

    Well it amuses me, so I thought I would invite reactions.
     
  7. May 21, 2013 #6

    WannabeNewton

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    Again, you can eliminate the coordinate singularity with a change of coordinates (see Kruskal–Szekeres coordinates) so I still don't see your point. You are also mixing up different solutions to Einstein's equation; cosmic time refers to the "time-like coordinate" of the preferred coordinate system of the FRW metric describing the universe - it isn't referring to "time-like coordinate" of a Schwarzschild black hole solution.
     
  8. May 21, 2013 #7
    What are the Kruskal–Szekeres coordinates at r = 2GM?
     
  9. May 21, 2013 #8

    WannabeNewton

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  10. May 21, 2013 #9
    Assume that I, and possibly other readers, don't understand what any of that means. Can you please solve the appropriate equations for r = 2GM and provide us values for V and U with r = 2GM?
     
  11. May 21, 2013 #10
    Just plug in ##r=2GM## in the equations?
     
  12. May 21, 2013 #11
    As I said, assume that I don't know how to solve them.
     
  13. May 21, 2013 #12
    There is nothing to solve... Just plug in ##r=2GM## in the definitions. This is just basic algebra.
     
  14. May 21, 2013 #13

    WannabeNewton

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    Solve what? You asked what happens to the coordinates at ##r = 2GM##. Just take the limit as ##r## approaches ##2GM## in the metric components given in the wiki article.
     
  15. May 21, 2013 #14
    No.

    If your friend Fred "fell" (past tense) into a blackhole and is perpetually red shifted at the EH, he still fell into the black hole for both of you. The photons bouncing off his poor spagettified self right before falling in are just stuck there, so all your seeing is an illusion. An afterimage of the photons still stuck just above the surface of the EH.

    If you want to speculate that the image of your friend is actually him just stuck in time on the edge of an EH, you might as well speculate that we live in a fish tank as well. (Just because you can't touch the edge of the fish tank doesn't mean it's real, right?)

    :wink:
     
  16. May 22, 2013 #15
    Thanks everybody. The inputs have been very valuable for me and I understand all the facts clearly.
     
  17. May 28, 2013 #16
    Hi Simon, thanks for your pleasant correspondence. I did review the link you supplied and though much surpasses my abilities, the information concerning black holes was very useful for myself and all who would be interested. Might I inquire of you a few questions as I hope you have the ability to respond appropriately, and it would help clarify my understanding.

    Do I understand correctly that you believe that there is no actual singularity, as it is only a theoretical construct?

    Do you believe there is no point without mass inside the black hole?

    Am I correct in assuming that black holes maintain different diameters in relation to the event horizon and that they can grow and shrink?

    If singularities exist, are not all singularities universally equivalent?

    Could you elaborate on the map verses the territory?

    Thanks again for any and all of your efforts.
     
  18. May 28, 2013 #17

    WannabeNewton

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    There are different ways to define a singularity. The most intuitive (but not fully accurate) way is to use the concept of time-like or null geodesic incompleteness. If a space-time contains a time-like or null geodesic that is inextensible in a certain direction (e.g. there exists a massive particle that ends its existence in finite proper time) then there will be a physical singularity in the space-time. The singularities won't actually be points in space-time; you can imagine that one has removed the singularity and a "hole" has been left in place. The problem is that the singularity theorems of GR provide no information on the actual nature of these singularities so they are not currently explained by GR; all GR can do is prove that these singularities exist.

    I'm not sure what you mean by this because the only mass parameter involved in characterizing a black hole is the mass of the black hole itself.

    The area of the event horizon of a stationary black hole can increase as the black hole's mass increases. The relationship is given by the 1st law of black hole mechanics (the area can never decrease as a result of a physical process if the null energy condition holds, this is the 2nd law of black hole mechanics).

    No, there are different kinds of singularities. For example, even amongst black holes there exist point-like singularities as well as ring singularities depending on if you are talking about static vs. rotating black holes. Things can get more abstract and pathological but there is no need to go there.
     
  19. May 28, 2013 #18

    phinds

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    Ron, Simon is being very generous. What he sees as poetic, I see as meaningless blather. You should read the rules. Unsubstantiated personal opinion is one of the things the rules talks about (prohibited). This is a physics forum, not a forum for poetry or blather.

    EDIT: this was a response to your post #16. I missed #18 and #19 and I see that you are not on the way to getting your facts straight. Still, my comments hold.

    FURTHER EDIT: I now see that Ron's original post and Simon's response have both been removed, making my comment about it here look strange, and changing the post #s.
     
    Last edited: May 28, 2013
  20. May 28, 2013 #19

    phinds

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    "Singlarity" just means "the place where our model breaks down". Models don't all break down in the same way. Also, "singularity" does NOT mean "point".

    The universe, in our most common model, is said to have started with a singularity and black holes are said to contain a singularity. These have nothing to do with each other except for the arbitrarily applied name.
     
  21. May 28, 2013 #20

    Simon Bridge

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    Just quickly - the link I gave you is a good starting place, you can google the bits that you don't understand.

    I know for a fact that it is an artifact of the model being used ... the same way I know the model spitfire hanging from the ceiling is made of plastic. There is no reason to suppose that the models we use are accurate in absolutely every detail so we have to be careful about how far we take them.

    When the observer is closer than the Schwarzschild radius, there is no reason to believe that anything much will be different. But there is also no reason to believe that all the mass/energy is physically compressed to zero size either.

    "maintain"?
    It is reasonable to expect that the collapsed body within the event horizon has a different diameter to the horizon if that is what you mean.

    However, you have to be careful with such glib statements - a lot of our intuitive concepts don't mean anything in these sorts of geometries.

    No. No more than all infinities being the same.

    "The map is not the territory."
    -- Alfred Korzybski (Science and Sanity, 1933, p. 747–61)

    The map–territory relation describes the relationship between an object and a representation of that object, as in the relation between a geographical territory and a map of it. "The map is not the territory", encapsulates the view that an abstraction derived from something, or a reaction to it, is not the thing itself. Many people do confuse maps with territories, that is, confuse models of reality with reality itself.

    "I pointed the Way and you fell down on your knees and worshipped my finger."
    -- Malaclypse the Elder (Principia Discordia)

    In this case the Einstein relations for gravitation are the map.
    Insisting on the physical reality for any result of these relations without checking them is to confuse the map for the territory. The map is always provisional.
     
  22. Mar 12, 2015 #21
    This is what I think finally.
    According to the General Theory of Relativity (GR), in strong gravitational fields, space-time gets considerably distorted, giving rise to time-dilation and length-contraction. Accordingly clocks near a black hole (BH) run slower as compared to clocks far away from a gravitational field.
    Let there be an observer (O) far away from a BH and let a traveller (T) travel towards the BH. The clock carried by T will appear to run slower and slower as T approaches the BH. As T approaches the Event Horizon (EH) of the BH (where the escape velocity equals c, the velocity of light) the time dilation tends to infinity. Thus O will observe T take infinite to reach the EH. In other words, O will never observe T actually reach the EH. At exactly EH, the clock of T (as viewed by O) would stop.
    On the contrary, T will smoothly cross the EH and fall to the centre of the BH in a finite time according to his own clock. He may not even notice anything unusual, while crossing the EH. But, if he looks back at O’s clock, it would appear to him to move faster and faster, until at EH, he would observe O’s clock moving with infinite speed!
    So far, whatever has been said above is well-known and incontrovertible. Now comes the paradox.
    The above-stated facts imply that O can never see any object actually cross the EH and, much less, fall into the BH. Since we, the observers on the earth, are more or less like O (the gravity of earth can be neglected in the context of any significant time dilation), the same applies to us. We should never see any object cross the EH of any BH, because in “our time” the process would take an infinite time. So, no BH’s should form in “our time”. If we extend the same logic further, no BH’s have formed since the universe has been big enough to have regions far removed from strong gravitational fields—say about 5 billion years or so.
    How, then, we have detected so many BH’s? There is incontrovertible evidence about a BH at the centre of our own Galaxy and many other galaxies. With a huge mass contained in a limited volume, they have to be black holes. How could that happen in “our time”?
    Open to correction, of course.
    Of course, the BH’s formed in the beginning of the universe may not create any paradox. But have no BH’s been formed due to supernova explosions or massive star-collapse in “our time” (for the last 5 billion years)?
    As far as I have been able to understand, the paradox may be resolved in the following way.
    When we detect a BH either in the centre of a galaxy or as a result of the collapse of a star, of course, we do not and cannot see any matter inside (or even at the boundary of) the EH for the reasons explained above. We infer the presence of the BH mass by the motion of stars around (outside the EH) the BH. If more than a certain amount of matter is confined within a certain radius, we infer that there must be a BH within that radius. This radius has to be slightly greater than EH, because it is impossible for light (and any information) to travel from the EH to us (in “our time”) on account of the infinite time dilation involved.
    Therefore, it is true that in the case of all the BH’s other than the primordial BH’s (formed in the beginning of the universe (when “our time” may not have existed), all the matter constituting the BH’s is still outside the EH (in “our time”). The older the BH, the closer the falling matter will be to the EH, but still outside it. That makes no difference to the gravitational effect of the BH, because the gravitational effect of a spherical shell is the same as that of point mass placed at its centre. In the case of a BH, all that we can observe is its gravitational effect. So, it does not matter where the matter is, as long as it is distributed symmetrically around the centre.
    In the case of the primordial BH’s, the matter may be inside the EH, though it is impossible to tell. In that case the entire mass of the BH may be at the centre. If so, we can say that at least one influence can make its way from inside the BH and come to influence us: gravitation. After all, the outside world is influenced by its gravitation.
     
  23. Mar 12, 2015 #22

    phinds

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    Well, what you have said all sounds right to me except that I do think you are making one mistake (or maybe you do already get this). When you say that all of the matter in a "recently" formed BH is, in our time, still outside the BH, that discounts the fact that we KNOW that the matter actually has fallen into the BH. The optical illusion caused by time dilation is just that ... an optical illusion that is accounted for. So while it's correct to say that we SEE the matter outside the BH with our eyes and telecscopes, it's not correct to say that it IS outside the BH "in our time". Looks can be deceiving :smile:
     
  24. Mar 12, 2015 #23

    Chronos

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    An infalling observer would not perceive a clock outside the event horizon to infinitely speed up - which implies the infalling observer would view the entire future of the universe during his brief [by his clock] journey. For discussion, see http://arxiv.org/abs/0804.3619, Falling into the Schwarzschild black hole. Important details
     
  25. Mar 13, 2015 #24
    [Mentor's note: Some "QUOTE" tags added to this post to make the thread easier to follow]
    To explain my point, I will give three examples:

    1 Let there be a star S, 10 light years away from us, at rest relative to us. The space-time involved is flat (or semi –Euclidian, more accurately) and S is in the same inertial system as we. So, both S and we agree on what ‘now’ is. Our clocks are the same. So, we can say that our view of S is an optical illusion, because when we look at S, we do not see it as it is ‘now’. We know that we are seeing it as it was 10 years ago. Now it might have exploded, but we will know it after 10 years. The same is true of observers at S.

    2 Now let S move with a relativistic velocity relative to us. Now, although the space-time involved is still flat (or semi –Euclidian), the frames of reference are different. We see S’s clock running slower as compared to ours’ and the same true of observers on S. Now we cannot say whose point of view is correct and whose is flawed. We and the observers on S are equally correct. Neither perception can be called an illusion. The situation is symmetric, because we see S’s clock as running slower and S’s observers see our clocks running slower.

    3 In the case of the black hole, the space-time involved between O and T is not flat. Near O it is flat, but near T it is strongly curved; and, of course, they are in different frames of reference. The situation is no longer symmetric, because O sees T’s clock running slower while T sees O’s clock running faster. We cannot say who is right and who is suffering from illusion. From O’s viewpoint, T never reaches the EH, while from T’s viewpoint, he reaches EH and the central singularity in a finite time (in fact for a BH 30 times heavier than sun, the time from EH to the central singularity is 0.0001 sec). But one cannot say that the viewpoint of T is correct and that of O is flawed, because they cannot agree on a common clock.
     
    Last edited by a moderator: Mar 13, 2015
  26. Mar 13, 2015 #25

    Nugatory

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    We know that the matter has crossed the event horizon in a finite amount of proper time along its worldline. However, you can't get from there to "actually has" without assuming some more or less arbitrary simultaneity convention, and this hidden arbitrary choice makes the word "actually" somewhat misleading here. How can I ever say that an event has "actually" happened if it is not in the past light cone of any point on my world line?
     
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