Friday, September 25, 2020

Black holes have no singularities

Lubos Motl writes:
But pretty much everything that used to look "singular" about black holes has completely disappeared in our modern understanding of black holes. The singularity at the event horizon is just a coordinate singularity, an artifact of coordinates. The singularity at the black hole center may be "more real" but you can't really measure its properties by apparatuses that survive for a suffficient amount of time. The black hole itself doesn't qualitatively differ from other "kinds of matter"; ...

The main message is "Please don't send me would-be deep e-mails about black holes if you still believe that the singularity is what is important in a black hole." Everyone who believes in this misconception is a 100% layman who hasn't started to understand general relativity (let alone quantum gravity) at all.

I agree with this. There seems to be a widespread belief that a new theory of quantum gravity will be needed to understand black holes. I think not.

On the outside, a black hole just appears like a heavy black planet. We can only see what is outside the event horizon. The event horizon requires tricky spacetime coordinates, but there is no singularity. If you go in past the event horizon, you cannot get out.

Inside that black hole, there is a much smaller (as viewed from the outside) region with a theory horizon. If you go in past the theory horizon, then our physics theories break down, and we have no idea what happens. Maybe there is a singularity on the inside, maybe there is infinite volume on the inside, maybe there is unification of all the forces, maybe there is supersymmetry, we just don't know. And we will never know, because we cannot get past the event horizon and report what we see.

Some wise guy is probably going to ask me why I have another blog called Singular Values if I do not believe in singularities? The answer is the title does not refer to infinities.


  1. Roger,
    Lubos is just moving the goalposts around (as usual) trying to score points with looking smart, but he forgets the history of his own profession. The 'layman' he is insulting happened to be the guy who invented the damn thing, it was David Hilbert invoked a singularity in his formulation of a space time black hole.

    'If you go in past the theory horizon, then our physics theories break down...', break down my ass, dividing by zero is not theory 'breaking down', that's not even theory failure, just broken arithmetic posing as clever, as physicists are no more allowed to do this math error than first graders. Spare me the complicated excuses that make this OK.

    Scientists in fact really have no actual idea what a black hole is outside of their diddling around with singularities which requires them to divide by zero and then play pin the tail on the donkey defining a 'Schwarzchild radius'. Look it up, they don't know what it is (their definitions are all over the map, and no one has actually taken the time to even read Schwarzchild's paper to see what he actually even said about it).

    The mathematical fiction of the singularity is far more important than linguistic trivia if you want your black hole the way it was postulated mathematically by Hilbert, NOT Einstein. Only by using non physical parameters (a point magically carrying mass without physical extension) can you even begin to get the required infinite density to push the hyperbolic math into the imagined shape of your 'hole' in the imaginary space time.

    Please do NOT conflate a theoretical black body with a space time black hole. They are different on many different levels, both structurally and mathematically, confusing them or treating them as interchangeable just muddles the topic.

    Newton proposed the black body, and defined it according to his laws of gravitation. A black body requires no 'curved space', 'mass points', 'infinite densities, 'space time', 'singularities' or other esoteric doublespeak drivel spiraling around a division by zero error. A black body is merely a proposed physical body with such a high gravity that even the speed of light is not sufficient to reach escape velocity. That's it. Newton actually did make calculations of escaping such a body at speeds exceeding light, as he had no reason assume faster than light speed was not possible. Do not elide back and forth between black holes and black bodies, they are NOT the same thing, never have been.

    If you want to do actual physics, stop jerking off with the word 'infinite', it solves nothing. "Infinite this", and "Infinite that", it's just plain old bullshit. There is no 'infinite' possible in science, how would you know? as you can not measure it, much less use it in calculation. Just say 'I don't know', and you will be far more correct and much closer to the truth.

    Walk before you run. If physicists want to do something remotely useful involving gravity, solve the three body problem. For all the blathering about how well they think they have a grip on gravity, they can't actually do the 'fiendishly difficult' math to solve a three body problem without resorting to fudging with sloppy approximations.

  2. Yes, I had read and enjoyed Motl's blog post too, when it came.

    Material properties like the specific heat capacity $c_p$ are dependent on many parameters like temperature. Such properties show a singularity at the phase transition temperature. For instance:

    The singularity appears only because the system description is incomplete, even if the physics of the change is well known. So, next time you watch a cube of ice melt in your glass, you are seeing a *phyical phenomenon* in action, and some aspects of its theoretical description has a singularity in it.

    Another type of singularity occurs in everyday physics, when you dip your finger in flowing water, and watch tiny suspended particles (say small bubbles, or dust-like pieces of grass) come closer to your finger from the upstream side, and when they come close enough, they suddenly skirt aside one way or the other, following a round-about path, avoiding your finger. No dust particle (if small enough not to significantly disturb the flow) ever hits your finger. Theoretically, even if viscosity were to be zero (as in the ideal fluid flow), there would be a point of stagnation---mathematically, a point of singularity.

    Another example: Take a channel and introduce two mutually immiscible fluids into it from two ends. Let the two inlets be ``off'' from the central longitudinal axis a bit. If the flow is laminar, you have a very simple singular *surface* that separates the two fluids. (For a turbulent flow, the singular surface still exists, but is far more complicated in shape.)

    It's been for decades that I've wondered why neither mathematicians nor pop-sci writers touch on *such* examples when they discuss singularities. The reason could be (i) they are sloppy, or (ii) they actively want to mystify physics.

    Singularities are useful. Their utility comes forth most clearly in the studies of nonlinear systems.

    Dynamical regimes are separated by singular surfaces. Yes, such singular surfaces (like all singularities) are a concept of *method*. They represent the *means* we use in order to distinguish the *abstract* quantities we define in our theories.

    Physically, however, it's only the qualitative behaviour which changes on the two sides of a singularity---i.e. for two combinations of the sizes of some physical parameters. But the singularity itself does not physically exist.

    In some theories of some phenomena, the physical space itself happens to play the role of a dynamical parameter too, e.g., as in the case of two immiscible fluid flowing in opposite directions through a channel. There still is no singularity in physical reality even in such cases; the singularity exists only in the certain mathematical models which we build for the situation.

    The term ``breakdown of physics'' is a bit overloaded. If, by ``physics'', you mean the theory which breaks down, fine. But if by ``physics'' you mean that the physical reality itself breaks down, then an absolute no-no. Physical reality never ``breaks down''. Indeed, it supplies the ultimate referents for the concepts and knowledge we use in physics---including the mathematical concepts. You cannot take these concepts, and use them to validate or invalidate reality itself. That's a gross inversion of hierarchy---and a gross stupidity.

    In short, singularities are only a methodological issue. They serve to delineate and distinguish the dynamical regimes of a theory (i.e. the ranges of combinations of parameters over which the same qualitative behaviour is shown, in following a *theory*).


  3. In the above reply, at the very end, I forgot to add the last sentence: ``Thus, singularities are mathematical objects which exist in mathematical descriptions, but not in the physical reality as apart from such descriptions.''

    I also found a very good URL that shows phase transitions and singularities that go with a phase-transition:

    Notice the 3D diagram at the top which *is* abstract, but the existence of the singularity is not immediately apparent, though you can make out that while there is no discontinuity of the zeroth order, there should be discontinuities of a higher order. Scroll down all the way, to the 2nd-order phase transitions, to see another abstract description that clearly brings out the singularity in the c_p vs. T graph.


  4. Ajit,
    Aside from the tiny division by zero problem which makes it mathematically useless and physically impossible,

    If you remove the singularity (infinite density and mass assigned to a diagrammatic point with no physical extension) from what is defined as a black hole, you don't get the ridiculous rubber sheet meets stiletto high heal effect necessary in your purely mathematical space time frame to produce a 'black hole'. Of course you can move your definitional goal posts all over, or just make up new definitions and pretend the old definitions were only just kidding, but it's still a load of bullshit with a shiny new suit of invisible clothes.

    Once again, solve the three body problem. That's useful, and will provide greater understanding of gravity we can actually use, and make you famous to boot, heck, you might even get on Oprah, possibly win a Nobel prize to put on the mantle.

    Screwing around with single mass rubber sheet models of the universe and fretting about the spaghettification of amazingly incautious hole poking astronauts and time travel is not useful, its just blather that makes for easy publication.

  5. CFT,

    Your rant does come with shades of humour, which did make me sort of laugh. However, I derive the definite impression that you seem to have too bad an impression of singularities, something which is not at all called for.

    First of all, I don't know about the black-hole singularity (to which you refer), nor do I care about that field. So, let's leave that scenario completely out of the discussion, and focus on singularities as such.

    In the fields that I do care about (or did), like stress analysis, fracture mechanics, composite materials, fluid mechanics, nonlinear science, electromagnetics, and QM, singularities *are* useful---so long as you remember that they are un-physical. But that is precisely how even *text* books on these topics present the idea.

    I will give an example: If you take a rubber sheet (like a gasket) and press it in between the two steel blocks, a theory practically used in engineering design (viz. elasticity) predicts a singularity at the interface between the two materials. See how---and how easily---engineers use this term "singularity":

    Here is a paper with some experimental photos showing the trend towards a singularity:

    Even simpler: There is a singularity in stress at any sharp corner.

    Yes, your point is well taken. An infinitely sharp corner does not exist. True. But that does not mean that the very idea of singularity is *completely* meaningless, or devoid of any purpose, or must be objected to every time it is invoked. We engineers regard the singularity at a sharp corner as just a limiting case of small radii of curvature. So, singularity (zero radius of curvature) provides us with a fixed datum for making comparisons---an abstract but well-defined datum, one that will never be realized, but is useful all the same. Check out this URL, for instance, to see how we use the idea in daily practice:

    In short:

    No, singularities cannot physically exist.

    However, at the same time, I don't (and engineers don't) share your almost religious zeal *against* singularities. That's uncalled for. We engineers use singularities as abstract theoretical data (plural of datum), as a concept of method, as a limiting case, but don't imagine that they physically exist. We leave the whole issue at that, but still use the concept the way the above URLs show.

    The problem seems to lie only with certain kind of physicists and pop-sci writers who write about such physicists and their theories.

    Therefore, I think, your efforts might be better spent arguing with *them*, rather than telling me (or to any other engineer who does understand the nature of singularities).


  6. Ajit,
    You are quibbling about something that wasn't even being discussed. I was clearly using the word 'singularity' in the context of use or misuse in the theoretical functioning of a black hole, not in any possible use of the word that has been applied in some other completely unrelated context.

    The scientific world is full of many of the same words used in many ways that have nothing to do with one another, it's one of the reasons science has fragmented so badly into squabbling little priesthoods and fiefdoms, as each little branch has become increasingly isolated in the use of terminology bordering on esoteric mysticism.

    If you wish to argue, let us argue about the same term in the same context, please.

  7. CFT,

    I don't know GR (and, for that matter, not even SR). However, from what I gather, the "may be more real" singularity which Motl talks about is a sub-type of the singularities I discussed. This "more real" singularity is a point singularity.

    Another example of a point singularity: An electrostatic force-field is regarded as being set up in the aether by a charged point-particle and a distant charged point-particle would interact with this field as it exists in the infinitesimal neighbourhood around its own position. This force field (strictly seen only by the second charge, not by the first charge) has a *point*-singularity at the position of the first charge. That's the classical electrostatics view.

    The salient difference between these two singularities is this:

    The "more real" point-singularity of the black-hole is enclosed by the surface of the event horizon. In contrast, the point-singularity of the Coulombic fields don't come with anything similar enclosing them.

    Next, as Motl points out, the event horizon itself can be seen as a kind of a singularity, because based on the GR calculations, anything that crosses the event horizon would be lost forever. As I understand, then, there is a surface singularity of the event horizon outside of the "may be more real" point singularity hidden by itself. This surface singularity is a bit more abstract in nature, in the sense, it seems to pertain to only some phenomena, such as whether something crossing it will ever return or not.

    The important implications which Motl discusses arise from such considerations.

    I have no knowledge of, and no interest in: GR, or the physics which determines the "more real" singularity, or the event horizon, or the issues of what to do with the proposals for physics of what happens beyond the event horizon, or at the inner (point) singularity, etc. However, I do gather a sense of these statements by Motl: "The singularity at the event horizon is just a coordinate singularity, an artifact of coordinates."

    My philosophical position is that an infinitely large quantity of anything cannot physically exist; that the concept is only mathematical.

    Further, my statements from my preceding reply, starting from "In short: No, singularities cannot ... " can be read also in regard to the black-hole singularities.

    ... I thought that all of what I said in this reply should have been obvious. It would be, to any one who knows about singularities. Reading your replies, I was just trying to be helpful. Not "quibbling". (Frankly, my very first comment wasn't even directed at your comment.)

    ...And, you don't wish to have a process of a never-ending comments stream here, do you?


  8. Ajit,
    again, for the last time,
    If you wish to argue, let us argue about the same term in the same context, not every other context you can possibly think of. If that isn't agreeable with you, we don't have anything to discuss.