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    Black Holes Demystified
    By Sascha Vongehr | September 21st 2010 05:18 AM | 17 comments | Print | E-mail | Track Comments
    About Sascha

    Dr. Sascha Vongehr [风洒沙] studied phil/math/chem/phys in Germany, obtained a BSc in theoretical physics (electro-mag) & MSc (stringtheory)...

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    Black holes draw audiences, because they are weird, they are profound, they are Albert Einstein and Steven Hawking rolled into a singularity. Or some such – except, none of this is actually the case. The black hole is a much more mundane concept, older than relativity, and despite much misinformation in popular and pseudo science, black holes have in a certain sense little to do with relativity (and I say this although and because I worked for many years on black holes and used general relativity when doing so).

    Yes, I know, our god Wikipedia claims in the very first sentence that “According to the general theory of relativity, a black hole is a region of space from which nothing, not even light, can escape.” This is not entirely wrong; it is just very misleading, and it leads people to go completely astray about black holes.


    Many people are convinced that there are no black holes without relativity theory, that black holes are somehow defined or must vitally involve singularities, that consequently black holes are just
    theoretical entities which have or cannot be observed, and even that any other approach to black holes, like the historical ones before relativity was around, have been crack-pot ideas.


    The weirdness and the fact that some phenomena is supposedly unobservable to science, all this is a slippery slope to mysticism and has no place in publicly visible discourse about science. That’s
    why the black hole issue is relevant.

    Let us get one issue out of the way right now, before even discussing escape velocity, which I will introduce below: A black hole is a body so massive that its escape velocity v exceeds the speed of light c.


    That’s it – no more – that’s what it was in 1783 already, and this is what it is still today, and relativity did not change a thing about it! Yes, you read correctly: this is still today the only and proper definition of a black hole. Read it again, learn it once and for all, and remember that it does not involve anything weird, like singularities or pathways to other universes, at all. Moreover, black holes are by now well known astronomical objects – they are out there and we have observational evidence.


    In the historical part, Wikipedia also gets to the fact that “the idea of a body so massive that even light could not escape was first put forward by geologist John Michell in a letter written to Henry Cavendish in 1783 …”


    It goes on to say “In 1796, mathematician Pierre-Simon Laplace promoted the same idea in the first and second editions of his book Exposition du système du Monde (it was removed from later editions). Such "dark stars" were largely ignored in the nineteenth century, since it was then thought that a massless wave such as light could not be influenced by gravity.”


    Now this may have been what most people or a large part of the science elite at the point thought, but that just means that people like the geologist John Michell had apparently a better
    understanding of physics then whatever group of famous names led the Wikipedia writers to employ the expression “it was then thought that”.


    The details can actually be understood quite easily: Escape velocity is the velocity that a body needs to escape the gravitational pull of a massive body.


    Escape velocity is quickly derived, if you allow me two simple equations: Consider trying to hurl an object, say a little pebble, so strongly that it leaves the earth and is flung out into space. In
    the picture, they use a cannon for that. The kinetic energy involved is proportional to m v2, where m is the mass of the body that you fling into outer space, and v is the velocity with which you throw it. The body must be flung at least as fast as is necessary to overcome the potential energy of the body in the gravitational field of the earth. That potential energy is proportional to m M/R.
    M is the mass of the big spherical body, like the earth or the black hole, from which we want the small object to escape. R is the distance from the center of the big body to the small object that we are about to fling out into space.


    What is so great about these equations? Well, you demand the kinetic energy to be at least as high as the potential one and see that the mass m of the small body falls out of the discussion! It follows v2 is proportional to M/R. The escape velocity of the object is independent of its mass m,
    and this holds regardless; however light the object may be, even if it has no mass at all and is as light as light!


    It was already known at the time (i.e. in 1783 and before) that light has a finite velocity, which we can express by the constant c. What John Michell got perfectly right is that if the mass M of the large body is sufficiently large, then the escape velocity v exceeds that of light: v > c. If light cannot escape, the massive body is totally dark, and that is your black hole, or dark star.

    Now some held the false belief that light does not interact with gravity. This issue was of course not well understood before the advent of general relativity theory. However, the very derivation we just went through should have told them otherwise. It would be wrong to claim that the proper interpretation of physics at the time would be that light does not interact with gravity, just because maybe many famous names attach to all kinds of misconceptions. Indeed, even when special relativity was proposed, many a good physicist was still trying to modify Maxwell’s equations; they were not all crack-pots just because history proved them wrong in the end. Scientists were neither sure about gravity nor about light. None of this diminishes Michell’s
    accomplishment: he interpreted the escape velocity equation correctly in the context of Newton’s universal(!) gravitation. He defined the black hole in a way that is still the proper definition today.


    What did relativity add? Relativity added two issues: Firstly, special relativity found out that nothing can go faster than light. Only in this sense does the “hole” aspect of the black hole become established by relativity. However, dear Wikipedia writer, NOT BY GENERAL RELATIVITY! The fact that light velocity is the limit is mere special relativity!


    What general relativity added is basically only confusion: If general relativity holds true inside the black hole, there could be, in some cases should be a singularity inside. This however is no more than a sign; a little red flag indicating that general relativity is probably not true far inside a black hole. A singularity is here related to an infinite (divergent) density. This is not weird, not philosophy, not time travel or warp drive, not worm hole or quantum healing, dear Hawking and Caroll and so on, although such silly interpretations do sell silly books. A divergence to infinity in a physical theory is no more than a sign that the theory has left its domain of applicability and should be replaced by something better in the future.


    Why do I ride on this singularity issue? I like to teach science properly, like in the boring universe,
    so that people learn something and do not just go home with their heads full of misleading rubbish plus the notion that I am awesome. People who are under the misconception that black holes involve singularities are also under the impression that black holes have not been found in astrophysics, and that is just wrong. It is well established  that there are black holes in every spiral and elliptical galaxy. The best observational evidence derives from our own galaxy, the milky way.


    So, the next time somebody rambles on about that he or she knows all about the mysterious physics of black holes, the answer is not “Ohhhhhha! Wow!”, but “Do you even know what a black hole is at all?”

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    Comments

    ananth
    "What general relativity added is basically only confusion: If general
    relativity holds true inside the black hole, there could be, in some
    cases should be a singularity inside. This however is no more than a
    sign; a little red flag indicating that general relativity is probably
    not true far inside a black hole"

    so, u r trying to say that general relativity is not applicable inside a black
    hole...which will imply that light is not the fastest (inside black hole), and something
    can always exceed its velocity and indeed can escape so called black hole.
    If this is the case how can we still call it a black hole if something faster than light can always escape from it.
    Is it really not necessary for a black hole to trap everything?
    vongehr
    "general relativity is not applicable inside a black hole...which will imply that light is not the fastest"

    It does not imply anything like that.
    ananth
    what could be the possible implication if general relativity doesn't apply far inside black hole.

    I thought like this...correct me if I'm wrong...

    The necessary condition for the existence of singularity is "nothing must travel faster than light".
    and for the nonexistence of singularity, light must not be the fastest..
    vongehr
    So why then does string theory work without singularities? (Rhetorical question - no answer necessary.)
    Neil Newell
    Hi sascha - Thanks for this article, I really enjoyed it (especially as it gave me an easy excuse to stop revising for my own astronomy/cosmology exam for a few minutes - we cover black-holes so its all revision really!) I can see that your definition "A black hole is a body so massive that its escape velocity v exceeds the speed of light c." is spot-on. However, there is also the issue of the density of the object. My revision tells me that the Schwarzchild radius (the radius at which escape velocity equals the speed of light and hence the radius of the 'event horizon') is given by R(s) = 2GM/c^2. (this could be derived from the equations you give in the blog). So, for the object to be massive enough that escape velocity exceeds the speed of light, its mass must be contained within a volume at least as small as the sphere of radius R(s). That means the object will be VERY dense indeed. The earth has a mass of about 6 X 10^24KG. So, if I've calculated correctly then the Schwarschild radius for the earth would be 0.009m, or just less than one centimeter. Any object of the mass of the earth packed into a sphere of radius one centimeter or less is pretty amazing! Sorry, but you can't convince me they are part of boring science - they are fascinating!
    vongehr
    Two aspects about the supposedly large density:

    Firstly: If you look at the super massive black holes in the center of galaxies, you will find that your calculation gives a very low density. Very dilute regions can become black holes merely due to their size. Just add more and more material. The mass M increases more than the radius R (since it increases with the cube of R), and at some point you have a black hole without ever having high density. In fact, the Hubble volume happens to be a black hole (if neglecting metric expansion) and the density is only one hydrogen atom per cubic meter or some such - vacuum basically.

    Secondly: density = mass/volume, but since space-time is strongly curved inside the black hole, you have no good handle on the volume. The volume is not the same as the volume of a sphere with the same radius (not even close, in fact, in some types of black hole solutions of general relativity, the volume may be infinite).

    Secondly is more severe than firstly: I would just forget about the density.
    Sascha,
    Very good article! It is refreshing to see this sort of explanation which avoids unproven assumptions such as singularities. I have been trying to warn against tacit assumption of the existence of singularities in many other forums! As you say, the assumption from GR is based on analytically continuing Einstein's equations beyond the horizon and the divergences should be treated as they are in other contexts, as an indication that the theory does not hold in that limit,or is fundamentally wrong.

    A quantum gravity theory or entropic gravity being correct should obviate the singularity. It has even been shown how non-singular BH states can be derived classically!

    There is also the question of how Hawking evaporation can occur in the case of "infinite energy density"? Hawking states a very long but finite evaporation time but wouldn't it imply an *infinite* amount of negative energy qubits??

    blue-green


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    I am more than happy to stay mainstream and show how General Relativity gives one a deeper understanding of black holes than can a Newtonian perspective.

    The calculation by Niel shows that the earth would have to be crushed to the size of a pea for it to have an escape velocity of the speed of light. I don’t know if the Victorians ever did such a calculation. If they did it, they would probably conclude that such a density is physically
    impossible and not worthy of further consideration. Without the vistas that General Relativity offers with its tilting light cones, they would guess that the structure of matter itself would prevent such a density from being attained.

    And so it was also with the big bang singularity. Few considered it to be realistic. It was presumed that matter itself would work its way out. It was felt that the singularity was merely a mathematical curiosity, the result of unrealistic spherical symmetry or other simplifications that went into the manageable solutions of the field equations. Solutions with a singularity were presumed to be special cases of “set measure zero.” It was not until Penrose and Hawking and a few others in the 1960s did rigorous proofs of singularities being a generic and topological necessity that these singularities became more than a mathematical challenge.

    Fifty year later, these classical proofs are still robust. The quantum mechanical corrections have not been worked out.

    Without the benefit of General Relativity one can be driven astray. A definitive book on the singularity theorems and proofs is The Large Scale Structure of Space-time by Hawking and Ellis in 1973. At the end of the book is a translation of Laplace’s proof “that the attractive force of a
    heavenly body could be so large, that light could not flow out of it.” There are some Newtonian whoppers in the proof. For example, it assumes that light will slow down as it leaves a gravitational field. In the extreme case, it is assumed to come to a complete halt.

    In truth, light in a vacuum always maintains its velocity c. Unbeknownst to Laplace, light is an electromagnetic wave solution of Maxwell’s Equations. Einstein and a few others noticed that Maxwell’s Equations are unchanged by a Lorentzian Transformation. It is Maxwell’s Equations, not Special Relativity that originally gave us the constancy of the speed of light. If Maxwell’s Equations are invariant under a Lorentzian transformation, then so should also be the general equations for motion. That was Einstein’s line of thought; it led to the discovery of a rich causal structure for spacetime and the realization that the rest mass for a solitary photon is zero. For two photons moving in opposite directions, however, there is a rest mass. Rest mass is not additive, not for light and not for ordinary particles. A Newtonian perspective will not give you that understanding, and yet, how else can one account for the missing mass and thermal energy released in a nuclear explosion?

    Our little equation in the opening essay for the matching of Newtonian kinetic energy and potential energy at the escape velocity is the following: ½mc^2 = GmM/R. If one honestly uses m=0 for light, one gets 0=0 which is not helpful. If one divides both sides by m as the opening essay recommends, one gets 0/0 = 0/0 which is an abomination. Without General Relativity, one cannot get very deep concerning gravitational singularities. You need the causal structure of light-cones and even better, tilted ones, which allow matter to lens and curve back on itself for things to get interesting.

    In Laplace’s original proof, he does not calculate a hyper-extreme density, as did Niel. Laplace calculates that light will not be able to escape from an object that has the density of the Earth and is 250 times the radius R of the sun. He doesn’t study the plausibility of such objects, yet he notes that if they exist, then “the largest bodies in the universe could remain invisible be to us.”

    A primary area where a Newtonian analysis leads one astray is with the parameter R. A Newtonian “black hole” has a finite radius. A general relativistic one, however, is a bottomless pit. The R parameter in General Relativity is more properly thought of as 4piR^2 or better, the AREA of
    the HORIZON of a black hole. R is proportional to the square root of the area. The Newtonian volume formula is going to underestimate any region that contains matter … and this, in part, is how General Relativity can accommodate extreme densities. Dense matter brings volume with it so there is not the naïve type of crowding and space filling that a purely Newtonian perspective gives. A pea-sized Earth is not so unimaginable with General Relativity.

    A purely Newtonian perspective will not give you an upper limit like c for the escape velocity. When matter is violently smashed together, the high density and rigidity can theoretically allow debris to fly out with arbitrarily high velocities and therefore have a chance of bouncing back out. Consider how when two crochet balls are touching and one smacks one of them, the other one flies out. Two Newtonian black holes can clash together and then separate partly destroyed with less total surface area than they had originally. This can never happen in General Relativity. The total surface area of the black holes can only increase, due to the tipping of the light cones
    outlining the causal structure from past to future. This one-way inexorable increase in the Total Area comes automatically in the full general relativistic treatment. It has led the way to the entropic understanding of black holes and gravity that we have today. A purely Newtonian perspective does not give us that vision.

    The precise definition of a singularity that is used by Penrose, Hawking and Ellis involves world lines that are not extendible in the future or past, not even on a maximally completed manifold. It gets complicated and technical. Be that as it may, it is worth noting that the singularities introduce uncertainties and destroy the classical determinism for which Laplace himself has been famously quoted. If you accept the possibility of singularities in the microfabric of space-time, then one has a reason to employ quantum mechanical methods, for example, Feynman’s Path Integral approach.
    vongehr
    "The calculation by Niel shows that the earth would have to be crushed to the size of a pea for it to have an escape velocity of the speed of light."

    Well, as I answered him, the calculation is also wrong and one does not need a high density at all.

    Long comment, but basically all besides the point I am afraid. Sure, you can stay "mainstream". That is always good at the time and would have put you right with those who thought black holes to be impossible when Michell proposed them. I prefer to stay with what is reasonable, and singularities are never reasonable. They may sometimes, because of our limited knowledge, be unavoidable, like in renormalization or even plain analysis calculus (infinitesimal stuff and all that), but it is nevertheless on principle unphysical and can never be operationally justified. I also like to stay close to what experimental observation actually tells us. It tells us that black holes exist all over the universe, but your big name singularities however only exist on paper.


    Oh, just one point maybe worth mentioning, about "Einstein and a few others noticed that Maxwell’s Equations are unchanged by a Lorentzian Transformation. It is Maxwell’s Equations, not Special Relativity that originally gave us the constancy of the speed of light."

    This is historically just totally wrong, since Maxwell's equations were thought to be holding relative to the ether. You cannot go back and change history with insights from today that they at the historical situation just could not know. As I wrote, plenty of good scientists tried to alter Maxwell's equation rather than invent general relativity. I guess, most of the people you like so much would have done exactly that, given the situation. Einsteins are a rare breed.
    blue-green


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    For reasons beyond my ken, my earlier post has vanished. Something mysterious is going on.
    Here is a copy of my first feedback ... a Newtonian friendly perspective that I offered before doing a more proper defense of the singularity theorems.

    [begin repost]

    The old work by Michell and
    Laplace on dark “stars” has long been known and acknowledged.

    What changes is its meaning and significance.



    I recently watched the YouTube cosmology lectures by Leonard Susskind. I was
    impressed with his back-of-an-envelope derivation of the FRW
    (Friedmann-Robertson-Walker) equations for the expansion of the universe using
    elementary Newtonian mechanics. (I might repeat it here if someone else does
    not do it .. and there is compounded interest).



    The derivation is so simple that it makes one wonder how the expansion of
    the universe from a state of infinite density was missed from the time of
    Newton’s Principia (1687) to Einstein’s publication of his field equations in
    1915.



    What a fantastic thing it could have been for Newton to notice ... instead
    of wading through the Chronologies of the Bible in search of whatever. Other
    stuff gets in the way ....



    There is tremendous explanatory power at one’s disposal when one can work
    with something as fundamental as the expansion of the universe. In hindsight,
    it is a bit surprising that it was not until Hubble observed it, that a
    universal expansion was considered to be reasonable or even thinkable.





    With black holes, the attention now is on their handling of information,
    entropy gradients and the non-local aspects of the information. These would be
    mystifying aspects for Michell and Laplace. Today the focus is on horizons and
    their temperature. These horizons can be the familiar ones of black holes with
    their blackbody radiation. There are also cosmological horizons due to the
    expansion. There is much debate as to the meaning and significance of these
    horizons and what they teach us about horizons and blind spots in other
    contexts. I find it all to be mystifying,

    challenging … and exciting.

    [end repost]

    my email machine indicates that there were more responses in this thread than what actually shows here .... many bits of missing information  ...
    which speaks volumes of general relativistic black holes ...
    and post Newtonian quantum mechanical ones too ...
    yet all is not lost.

    vongehr
    "The derivation is so simple that it makes one wonder how the expansion of the universe from a state of infinite density was missed from the time of Newton’s Principia (1687) to Einstein’s publication of his field equations in 1915."

    Because infinite density is nonsense. Newton knew that, Einstein knew that (that's why he initially put in the cosmological constant - he only later changed his mind, due to Hubble's discovery), and we nowadays also know that, since there is no infinite density at the start of the universe (there is inflation before the big bang).
    blue-green
    Normal 0

    Sascha, it was not (as you indicate) because of a mathematical singularity that Newton (or Einstein) failed to properly predict something so wonderful as the expansion of the Universe. Something else got in the way. Newton was more than a little comfortable working with point-sized masses and all. That was the very essence of his program. Calculus let’s one shrink an entire planet (or star) to a point for the sake of doing calculations. 

    I also stand by my other notes. Let us know when you publish a disproof of any one of the singularity theorems by Hawking or Penrose (which by the way, do not talk about infinities at all).

    Scientists know that infinities cannot be taken realistically (although Einstein himself was guilty of postulating an infinite time in his cylindrical cosmology). Exactly how to handle infinities and lop them off is an open challenge. Feynman was a master at it, yet he considered his methods to be no nobler than sweeping dirt under a rug.

    Mathematical purest look down upon the cavalier way that physicists use and misuse infinities. They wrung their hands over Dirac’s Delta function, yet one can stand in the way of progress for only so long.

    Is an electron a point-like charge? No, of course not. Yet the model is quite handy.
    vongehr
    first off, if you are trying to tire me out, you may be better off at whatsupwiththat or realclimate. Pick a side, doesn't matter which, and then go have your type of arguments going. I am not going down onto that level.

    Nobody was ever shrinking anything down to a point just by using the location of center of mass in an equation.

    Nobody ever, certainly not me, ever doubted the GR internal singularity proofs. Go learn to read.

    And your big name dropping also sucks. In case you think you make yourself respectable by putting every famous MFer ever alive in one comment: Wake up.

    You may now go back and read my original post, which is written on the lines. First read the lines, afterward you may try read in between the lines, which you are apparently no good at.

    (to anybody not sensitive enough and who is wondering why I am short and unfriendly to this commenter, start with the sentence "Let us know when you publish a disproof of any one of the singularity theorems by Hawking or Penrose" and then go on to less obviously passive aggressive statements that seem oh so highty mighty, and maybe you will get why I already did not like his first comment. And yes, I usually delete crap comments like this - just happen to have a very tolerant day today)
    blue-green
    Normal 0 Sascha, you have not even begun to explain why it took so long for the universal expansion to be derived, at least on paper. If could have been done (semi-rigorously) by Newton and the generations that followed him. If this had happened (and maybe it did and was overruled), then the development of telescopes would have gotten quite a boost in funding. Instead, here we are 300 years after Principia Mathematica and just now,  refining our theories with inflation, zero-point fluctuations and colliding branes. We could be generations further down the line. Since the most fundamental aspect of black holes was known centuries ago (by your own reckoning), why did we have to wait until 1929 for Edwin Hubble (another name drop there) to give us convincing evidence that the fixed stars are not fixed? If there is something wrong with me using an open mike to ask this question?      
    vongehr
    "you have not even begun to explain why it took so long for the universal expansion to be derived"

    Why do I have to explain metric expansion after a blog post on demystifying black holes?

    Expansion is not something appealing without very good evidence. After all, space is something (vacuum has properties), especially to most people before us (ether), so if it expands, where the hell is it all coming from? Although space is mere emptyness in the Newtonian and the GR equations, that does not mean that Newton or Einstein thought about the fundamental nature of space in such a way. Even for Einstein, space reacts dynamically to the energy density, so it is something physical. It is your personal and very 1920-1970 kind of favorite interpretation that the fundamental nature is purely abstract relative arrangement of events with nothing actually happening (during time) at all but instead mere consistency (block universe). I agree, somesuch is the very (very very!) fundament anyways (consistency of phenomenal consciousness), BUT we are very very far from that level in today's physics. Even today, space is something, the vacuum condensate, the Higgs medium. Thus, it is still today counter-intuitive that it just grows and grows.
    This is totally fascinating, I'm not much on the math but i do think about this stuff alot. I'm just going to throw my thoughts out and ask for an opinion. In order for the universe to expand , it will need an energy source. The expansion itself is the energy that feeds another energy in which i thought would be the black holes. In other words,the compression reaches a point of zero and creates an explosion of energy , hence a black hole. The black hole is the energy sorce that creates suns. As this energy is released it helps fuel the expansion. Compression and expansion.

    vongehr
    "In order for the universe to expand , it will need an energy source." No it doesn't