Wednesday, February 12, 2014

Can Planck Stars exist?

Carlo Rovelli and Francesca Vidotto recently proposed a bold solution to the black hole information loss paradox and the firewall problem that they dubbed Planck stars:
In a nutshell they are suggesting that the horizon of the black hole vanishes, due to quantum gravitational effects, at a radius much larger than the Planck length. They call the remaining object a Planck star.

To understand why this is a really radical proposal, let me first give you some context. When matter collapses to a black hole, its radius shrinks and its density increases. Quantum gravitational effects are expected to become strong when the curvature reaches the Planckian regime. The curvature is the inverse of a length square, so that means the curvature is the inverse of the Planck length square or smaller. At which radius the collapsing matter reaches this regime depends on the total mass: The higher the mass, the larger the radius.

The radius at which the collapsing matter reaches the Planckian regime is larger than the Planck length if the mass is larger than the Planck mass. The radius is however always smaller than the horizon radius, so it doesn’t really matter exactly what happens because it’s not in causal contact with the exterior. The curvature at the horizon is weak as long as the total mass of the black hole is larger than the Planck mass. This is somewhat unintuitive, but the curvature at the black hole horizon goes with the inverse of the mass square, ie the higher the mass of the black hole, the smaller the curvature. Thus the often made remark that you wouldn’t notice crossing the black hole horizon - there’s nothing there and space-time can be almost flat if the black hole is large. In particular, you don’t expect any quantum gravitational effects at the horizon.

But the mass of the black hole decreases due to Hawking radiation. Keep in mind that Hawking radiation is not a quantum gravitational effect. It’s quantum fields in a classical gravitational background, a combination often referred to as ‘semi-classical’. If the mass of the black hole has shrunken to the Planck mass, the curvature reaches the Planckian regime and that’s when the semi-classical limit breaks down and quantum gravity becomes important. At that point also Hawking’s calculation breaks down and information can be released. However, the standard argument goes that by this time it’s already too late to get all the information out. Details are subtle but that’s a different story. Suffices to say that Rovelli and Vidotto want information release to be possible earlier, when the radius of the black hole is still much larger than the Planck length and its mass much above the Planck mass.

The only way to do this is to have strong quantum gravitational effects in a region where the curvature of the semi-classical metric is small, much below the Planck scale. In the paper they don’t explicitly say that this is what they do, but of course they have to. You see this most easily when you look at the metric they suggest, equation (14). The third term (containing α) is the correction term that supposedly has a quantum gravitational origin. The validity of the semi-classical limit means essentially that the third term should be smaller than the second as long as the second term is smaller than one. If you convert this into inequalities you find α < m, and that is explicitly the situation they do not consider. Instead α is supposed to start at m and then increase. They do not give any reason given as to why this should be so or what the meaning is of α or what the necessary source terms are for that.

At this point you are probably ready to throw the paper away. There is a reason one of the postulates of black hole complementarity is the validity of the semi-classical approximation near the horizon of a black hole with mass above the Planck mass. That’s because the curvature there is small and no quantum gravitational effects are at your disposal to screw up the semi-classical limit. However, allow me to exercise some good will. I think what Rovelli and Vidotto suggest may be possible if the Planckian-density core behind the horizon displays a very unusual behavior, though that’s a big “if”.

The behavior would have to be such that as the total mass is shrinking, the mass is taken from the center only, leaving behind an increasingly thinner shell of high density at a constant radius (or even an increasing one). This shell would eventually intersect the horizon of the black hole and could do so conceivably at a radius much above the Planck radius. This isn’t a priori in conflict with the semi-classical limit because there is a high density now and also a high curvature region.

However, the metric that is used by Rovelli and Vidotto does not describe such a scenario. (The metric inside a shell has to be flat while their metric is actually singular at the center.) Besides this, there exists no approach to quantum gravity that suggests such a hollow-core behavior. There doesn’t even exist a model that describes such a situation. I also strongly suspect that such a solution, even if it can be created by help of some quantum gravitational pressure (this is almost certainly possible), would be unstable under non-spherical perturbations and just recollapse to form a smaller Planckian-density core. Iterate and end at Planck scale radius as usual.

In summary, this is an ad-hoc proposal. It is not based on anything we know of quantum gravity. Neither is it a complete model. I am reasonably sure that the metric they use cannot describe the situation they want while still maintaining energy-conservation. They do not calculate the curvature that belongs to that metric to check whether their modification is consistent. Neither do they calculate the necessary source that presumably contains a quantum-gravitationally induced stress-energy. It is an interesting suggestion, but I do not think it is very plausible. Planck stars almost certainly do not exist.

Acknowledgements: Carlo Rovelli has been very patient explaining his idea by email, but as you can tell I’ve remained unconvinced...


  1. Hi,

    A basic question: Why does the radius decrease when mass fall into the black hole? It should mean that the total mass is increasing, so why not also the radius?


  2. This comment has been removed by the author.

  3. Thanks for posting this, Sabine. Following the invitation you sent me at the end of our discussion, I summarise here briefly the reasons of our disagreement, as I see them.
    First, the core of our suggestion is something that you do not mention: if in Nature there is a phenomenon as we consider, this could be observable, and we indicate a way for observing it. This makes a big difference, and is the main point.
    Second, all possible solutions to the Black Hole information paradox require some counterintuitive physics. The phenomenon we suggest is probably less counterintuitive than other proposed solutions of the paradox (and unlike others would be observable).
    Third, I think you mix up a bit the fact that an equation has a small correction term with the fact that the correction in its solution is small. If an equation has a small correction term, the difference between the perturbed and the unperturbed solution can become very large over very long times. This is what opens a possibility. This possibility indeed, we have later discovered, has already been considered by many before us.

    Congratulations for your blog, carlo rovelli

  4. Nidnus,

    This is probably a misunderstanding. The horizon radius increases when mass falls in. I don't know why you think otherwise? Best,


  5. Carlo, I really dig the "comments" on this paper at arXiv. :-)

    Let me also take this opportunity to call attention to this wonderful paper of yours which everyone interested in cosmology should read. Has it been published anywhere other than at arXiv?

  6. Sabine, I find this a most refreshing new post.
    The more we pile up bricks the larger the mass so it is surprising that more mass can mean a smaller radius.
    Such info or light escape seems to come somewhere in scales in between where we imagine a singularity inside a black hole or temperature / entropy as a hollow centered structure. We need at least a multi shelled structure like an nucleus or proton.
    If parts of this is true say c or h as the center scale as volumes, might this issue explain the small portion if a nuclear mass contributed by the Higgs so imagined as a central singularity?

  7. A decade or two ago, Kenji Hotta published a suggestion that black hole formation was associated with a with a string theoretically motivated phase change that produced a zero mass, zero entropy nucleus surrounded by a thin crust containing all the mass and entropy at the horizon. This notion might have something in common with Rovelli's as you describe it.

  8. "The higher the mass, the larger the radius." Black hole external radius increases as mass. Black hole external volume increases as mass^3 (not as the cube root). A large (galactic core) black hole has asymptotic zero density. A Kerr black hole with a central singularity has no origin for its immense angular momentum, e.g., Milky Way black hole GRS 1915+105 at 1150 Hz.

    Speculate that a large mass-equivalent resides at externally viewed large radius. (What does information mass?) Physics is nonplussed by heretical empirical inputs. Opposite shoes vacuum free fall non-identically. A geometric Eötvös experiment opposing 20 grams each of left-handed and right-handed alpha-quartz compares 6.68×10^22 pairs of opposite shoes (pairs of 9-atom enantiomorphic unit cells). Do the experiment, falsify Official Truth, start the healing.

  9. No mention of non-relativistic MOND in the references from the Rovelli/Vidotto publication — Milgrom, McGaugh, Kroupa, & Pawlowski have shown that something is EMPIRICALLY WRONG with Newton-Einstein gravitational theory. BLACK HOLE GURUS CONTINUE TO IGNORE SOMETHING ROTTEN IN THE FOUNDATIONS OF THEIR WORK.
    "It is always possible to fit a dark matter model to data. That is not the same as the data being predicted by the dark matter paradigm." — Stacy McGaugh

  10. The evolution of this developing scenario has to meet a geometrical propensity in the nature of the collapse? Does it? It is as if there are statistically trying to nail down an obvious affect in the dilation process?

  11. What I mean is that if Higgs is statistically significant in the energy range establish, the such affect has to be relevant in the nature of the collapse. This has to be already seen a number of times to make is considerable as a affect in the cosmos?

  12. "At this point you are probably ready to throw this paper away".

    No, No, I love prestidigitation.

  13. How would one represent imaginary spin? The faster something moves the more it stretches out? Can we ride a saddle without a horse? Would passing by a globe at the speed of light would we briefly see the same side yet never surround it? Is a point as now between past and present light cones real or imaginary or as a concept distinct singularities as such? As a circle expands to an infinity thus a flat line in the spacious now does movement along such a quadratic circle matter π ratios absolute to scale, or is time and cause as we imagine it independent and outside such effects observed as affects?
    I do not suggest such primitive thoughts can be shown formal in any dream of theory, but as said of a near or distant God, a geometer, something we imagine beyond the maths could be there. Only said deity is just a magician and our theories are part of the stage and science is concerned about how the trick was done, we between curtains rise or fall and part if the stage if not the play, and if it is a trick.

  14. This is a really good post. Concise, doesn't talk down to the reader, but written in clear enough language to get the argument.

    Still seems like a lot of hub-bub over something no-one can conceive of an experiment to test anyway...

  15. The relativistic nature had to be expressed in the particles themselves, and not as, the mass less photon determinations of a black hole?

  16. Regarding "The behavior would have to be such that as the total mass is shrinking, the mass is taken from the center only, leaving behind an increasingly thinner shell of high density at a constant radius" - wouldn't an exterior observer always see all of a black hole's mass as existing at the horizon, since they never actually see anything pass through?

  17. M*P*Lockwood,

    Depends (crucially) on where the observer is... Best,


  18. /* there exists no approach to quantum gravity that suggests such a hollow-core behavior. There doesn’t even exist a model that describes such a situation */

    Chapline and Laughlin before some time proposed similar scenario too. It follows from real life experience, that at the case of common massive bodies the highest curvature of space doesn't reside at their center (as the general relativity follows), but at their surface.

    You may not want to call it the quantum gravity effect, but IMO the QG deals just with phenomena at the human scale, so I don't see anything controversial with such a labeling. From AWT perspective such a solution corresponds the Kerr solution of BH with toroidal singularity at its center, rather than hollow sphere.

  19. "It is not based on anything we know of quantum gravity."

    Dear Bee,

    A little tongue-in-cheek, may I suggest that we know nothing of quantum gravity? (OK, we know many things that we can confidently say are not quantum gravity, but apart from that?)

    In the same vein, one more thing to note - that the Planck-scale is significant is something that arises from numerological arguments of the type that have failed us with regard to the cosmological constant; and with regard to SUSY. Perhaps progress in quantum gravity requires utterly shedding the ideology of the Planck scale.

    With best wishes,

  20. ^^^Well, I should say one should be skeptical of the Planck scale. Certainly there is some scale at which quantum gravity effects become important, but that scale is 10^x * conventional Planck scale, where failure of our naturalness arguments may mean that x can be significantly different from zero.

  21. Dear Arun,

    We do know some things about quantum gravity. For example that it's very weak where we sit. And we sit in a weak curvature region. The curvature at the black hole horizon doesn't have to be any larger than where we are now. The CC is a long-distance issue, while we're talking local short-distance effects here. In spirit I agree of course with what you say, we don't know much about quantum gravity, so we should be open-minded. But as I said, it seems to me very implausible. Best,


  22. Extracting from the abstract of a 2012 preprint by Steven D. Bass:

    "The vacuum dark energy density extracted from astrophysics is 10^56 times smaller than the value expected from the Higgs potential in Standard Model particle physics."

    Or in other words, if we attempted to estimate parameters in the Higgs potential, using the observed value of the cosmological constant, we'd guess wrong by a factor of 10^56.

    Yes, I know this argument goes in the wrong direction to be interesting for quantum gravity - but given the low energy value of G, the usual guess of the scale at which quantum gravity effects become important might be similarly off by a factor of 10^something.

  23. Arun,

    Well, if the Planck scale was at a TeV, we should have seen quantum gravity together with the Higgs - and we haven't. Be that as it may, lowering the Planck scale in and by itself doesn't solve the BH infloss problem and it also doesn't change anything about the argument that I gave here. It just moves the notion 'strong curvature regime' to a different energy (density). Best,


  24. Arun good comment

    Lost post trying to edit one surplus letter.

    Surface or singularity say Tori in Tori at a center does not save a particular models face in view of new cognitive connections or experiments.
    Like a firewall where old theories crumble into uncertianties that then seem not an accidental certain but narrow vision.
    The depth if what are the foundations of that invented or discovered as physics distinct from mathematics or not, is like an amoeba drawing in its pseudopods into a sphere that can call all outside itself a fortress against crackpottery.

  25. Philip,
    there is a discussion of Carlo's paper on cosmological constant on cosmocoffee

  26. Dear Bee,

    Agreed, whatever the Planck scale, the black hole problem still remains.

  27. A simple, natural theory demonstrates that:

    - the vacuum energy densities of the microcosm and macrocosm are indistinguishable

    - there are no hierarchy problems in particle physics

    - gravitation has the same strength and physics in the microcosm, macrocosm and cosmocosm.

    Here is the paper.

    The key idea is that General Relativity must be further generalized to include global discrete self-similar scaling.

    Principle: Global discrete relativity of scale. There will be no progress in quantum gravity efforts until this idea is dealt with in an open-minded and objective way.

  28. Robert, great and relevant thoughts in that 2009 arVix. I agree with the principle but not that GR is radically changed when generalized. (my term for it was Exxene), especially as a quasifinite locality region also suggested by Sabine is sufficient in the physics of our region to support in entropy life and civilization.
    I just read her links to ideas of reality as a simulation (again does it matter for predictions if we can only have one region simulated and closed in the whole observable universe as the link article suggested, a Platonic cave of sorts where a virtual machine has trouble thinking it is not hardware and no hierarchy in program running is necessary.) Why would a civilization want to go far into the stars when the physics say inside a quasar is more wonderful to explore and can be physical as we peek out from our caves?
    But my estimation of your ability grows. Thank you.

  29. The fact remains that particle decays have to be entertained in the scenario presented, this may come after the collapse, to a limit where the structure of the black hole comes into play, this as an energy correlation is reached? The particle decays must work backwards as to describe the energy source of the geometrics involved?

  30. Dear Bee, it is rather mind-boggling that matter degrees of freedom some how excite quantum gravity degrees of freedom as the black hole shrinks down to Planck scale. The requirement of asymptotic freedom in QFT seems to imply that the matter degrees of freedom are only very weakly coupled, so they cannot by mutual interactions combine to produce Planck-scale structure that might produce Planck-scale quantum gravity excitations.

    I really hope you physicists figure out the answer during my lifetime, and before I'm too senile to understand the answer.

  31. Robert etc al,

    I seed a paper today suggesting a revisiting of the idea of white holes. The singularity of the big bang said the only such object we might assign the name.
    A lot has happened and yet little has changed since Hawking chose to look into the Steady State and Big Bang universe debate.
    In this wild west explosion of highly speculative papers instead of concepts they contain lost in the crowd of them we should explore their evolving connections at face value including papers from the same institution that deeply suggest contradictory conclusions.
    perhaps, in these matters of general singularity what we think of as information does not exist. Where then is the paradox?
    when we try to define it we may mean our models predicting identities and differences.
    A more general principle, Robert, I call the Quasic principle. Meaning as well as any scale as singularity in this sense may not exist either as beyond metaphysics leaving stereonometry (Aristotle's "lost " book) as the foundations of models of our cognitive realms of mathematics and the physical.
    Imagine then we have two ideas and issues of how and to what extent they are related. Gravity and Matter.
    Let us say we have two spherical objects, hollow or not. Nothing can escape from inside either one but they can be considered the same surface.
    Gravity involved or matter may be discrete or continuous. Think walking on the moon we go make an impossible turn and instantly wind up somewhere on the earth.
    How else would we describe the inside or outside of things let alone reflections and reversals such as of time? We do observe phenomena explained by some hierarchies and self congruent modeling, the neutrinos do it. A signal can be imagined arriving before it is sent. Matter can be transferred at a distance and so on. While our models turn out so ultimately simple the scientific phenomenal universe is understated as vastly more complex. This does not stop us from beginning to make or revisit old theories as the pendulum swings into unique or a multiverse of multiverses in contemplation or the one as nonnecessary reality with hidden paths of necessity not forbidden as even shows the working paradox of chance. Best

  32. What we desperately need is an empirically well-motivated and highly testable general paradigm that can explain current enigmas, remove the seven shortcomings of the standard model of particle physics, reveal the correct approach to making GR and QM compatible, and offer a unified physics for all of nature.

    What we do not need is more argument from authority, taking assumptions on faith, obscurantism, mental diddling with imponderables and metaphysics, or more blindly following those who have lead us into the current swamp of confusion and disarray.

    If we are not interested in new ideas and thorough questioning of old assumptions, then we can only hope for some stern guidance from nature.

  33. I took a cosmology class at UVA ca. 1975. When black holes came up, I asked ~ "wouldn't quantum mechanics [uncertainty] prevent a literal point singularity from forming?" The prof answered to the effect, it's a good question but they didn't understand how to apply QM in such a case. I'm gratified that such issues are getting hot.

  34. Dear Arun,

    Oh, but I have already figured out the answer: Gravity is asymptotically classical and also decoupled from matter. No singularities, no non-renormalizability, no bh infloss problem. You can read this as a variant of ASG. See, I've solved it all - unfortunately nobody cares. In that, I am very sympathetic with Zephir's struggles... The difference between us is just that my paper was published in PLB :p Best,


  35. Dear Bee,

    Then I'm going to read your paper very carefully :)

  36. Sabine,
    Thanks for the link to your formal paper.
    I agree with sympathy for theorists in this human attempt to inquire and solve questions, perhaps see s few moves ahead.
    But your grasp of the problem shall I say is a qualitative leap above the rest.
    Hawking adapts and should have credit for a new seemingly trivial design element of a periodic table of black hole like entities.
    What about a BH star of pure strings or pure singularities should we sympathize or feel held back by beautiful yet less advanced terminology?
    The concepts as branes do better but applied without your questions of locality - non locality what do get in the context but published models such as charged branes or intersecting ones as if epyrotik cycling theory?
    Reading you has given my own math recreations a certain dynamism that gives me a wider base to comment on what models will be more sensible in physics. I can thus better judge and sympathize with less doubts for unexpected certainties we seem to have.
    Imagine absolute two or more spheres nothing escapes yet one surface at a distance. On each we have areas which are branes thus whole new general effects between them nearby to say beyond into a scale where the stars stand out thus night
    That was my last thought so inspired before I know I need a rest from being so inspired.
    Arun, this is happening in your lifetime but I have little doubt we will all find what she and others seek beyond this day, and long for more.

    Best of the Best from but an imperfect poet not sure what perturbations mean, like Whitman auditing university lectures :-)

  37. Zephir and others with insights raised by flat or curved space generality.

    Breaking news I just encountered from friends with a more Platonist sacred geometry stance. But look up Goldberg Polyhedra for this fourth class of solids. It concerns dihedral angle discrepancy herein three space. Add that to your list of black hole objects Zephir, not a structural approximation for a more general model where mathematics does seem to apply with certainty to physics, a question Einstein wondered why. Just where would such curvature go if lost or hidden physically?
    In actually constructing ball and stick models that seem independent of scale for patterns (of touch) we can imagine impossible structures. The author of this news applies it to viruses as a suggestion. Then are papers on graphene superconductivity far away, or on special chiral effects of new forms of particles. The shadows from 5D into 3D also have faces slightly convex as approximate by which electrons flow over atoms.
    Slightly concave properties exist also near Flatland with self or no need for renornslization in holographic divergent hullabaloo.
    If we do want to explore this evidently no end to difficult theories, just as the golden ratio is special in four space the begin in flat five space by replacing the square root of 5 in the quadradic by the square root of 11.
    Happy computations. I hope all this is important yet even at the zero Plato polytope where does our story end?

  38. Arun and Sabine

    The paradigm is Mp Lp = h

    For a paradigm shift you need much more than wild unfounded speculations

  39. Giotis, assuming there is a paradigm shift and our concrete model can be falsified, just when do we pass that event horizon? QGR seems natural and straight forward that continues issues of physics as linear or curved. A long sought solution to a goal of physics unification if possible. Is geometry as principle a clear statement where math meets the physical or not, the how and why in Euler's formula algebra was unified with geometry. I do not know just how much is new of LQG as original new conclusions given one instance, one photon, one universe or thinker as we all in effect are inside of. Can we not generalize Euler's insight, it is perhaps the most beautiful equation but is it art? It is easy to ultimately defeat logic as logicians know behind the screen but it is much more difficult to design a logic system to show why. What is the basis here for your objections?

    Zephir, that description could be seen as the actions from outside determining the galactic inside of a quasar too, or electron motions at an paradoxical anthropic distance the escape events in an atom 's nucleus.
    Some suggest we are 65million years from the center of the universe which is hard to picture if everything is more distant mutually on an expanding sphere. Gravity close to Matter or not may be CC distinct or not by such higher dimensions of a gravitational or particle worm hole moebius or mirrored mass Tori as we fall thru quantum slits as blind as third observers.
    We avoid yet survive the big crunch of singularity, a cyclic universe whose source of energy irrelevantly does not decay. The ekpyrotic model says as much, two flat branes and a cigar shaped timelike or galaxy like symmetry region. But is this not a question of what is flat or curved aethers? That two planes can be two balls? Ancient numbers had gender not just even and odd, 2 x 3 = 6 in compact models of standard and modern families where lust meets love in the brain at the place of making beautiful music together. One view is too narrow as this generation of stoned robots erect swan like confusions in their black or white feathers. Penetration is penetration no matter how deep.

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  41. "Here is the paper."

    For the benefit of the innocent, I must ask whether the paper has been published in a reputable journal.

    It references older papers which made testable predictions which however have been ruled out in the meantime. As such, the foundation on which the paper above is built has been eradicated.

  42. Phil,
    I suppose different people with some growing learning and a philosophy of science that may or may not make testable predictions that wonder about coincidences or rule models out, is another form of peer review.

    The issue of not finding Higgs and it placed in some parallel place of metaphysical unknowns as with some SUSY would not scientifically rule it out. Our working hypothesis becomes again a working paradox.
    Consider Hogg's honest research in relation to Robert's link. Looking back I feel naieve at things Googled that I posted in blog comments that from my own system reads now to me as independently innocent at worst. Evidently emotional stability is healthy for good dialog in research.
    Why did Hogg say we can rule out a fractal grounding in his attempt to interpret astronomy data better by statistical core methods.?
    From my quasic view his was an attempt to try a Peano curve on a 256 x256 8D grid. But there are other such curves made of linear elements that would fit or even be superimposed for effects more general between cells and subsets of symmetry.
    The problem then is one simply of finding the right curve order to fit a reduction to a physical reality. We generalize self similarity where information as fractal and holographic description is both or either ruled out or equivalently both are generally conserved containing each all such information. The Feynmann reduction while it has its place is not the only center view between QM and GR.
    arXiv rejected Peter Rowland BTW. I think the rate of progress of his sci am published work in the book club suffered for it.

  43. Zephir: I warned you. You have one comment per post. Chose it wisely.

  44. Giotis,

    Not sure what you're trying to say. This isn't a paradigm, but true by definition. Best,


  45. Your paper is compatible with this definition then?

  46. One does not expect open-mindedness and objectivity from the Rush Limbaugh of physics.

    One expects misinformation, diversionary tactics, and heavy bias.

    And that is exactly what one gets.

    No discussion of the physics.

  47. Hi Giotis,

    Oh, sorry, I thought you were referring to Arun's comment about lowering the Planck scale etc. No, in my paper this relation is not fulfilled. The mass scale is fixed, the length scale changes. (Relative to the 'normal' value of the Planck length.) Best,



  48. Is it so hard to imagine that information on any scale could be so degraded that it could be destroyed/lost, for all practical purposes?

    Most "firewall/BH" dithering begins with an unsupported statement that quantum unitarity requires that information not be lost, or something like: 'pure states cannot morph into mixed states'.

    Is this purely an abstract theoretical assumption, or is there solid empirical evidence for this "quantum unitarity"?

    Has the latter been subjected to sufficient scientific skepticism.

    Is it an ABSOLUTE certainty? It certainly seems to be treated as such.

  49. Robert, your last post got me thinking and I woke up with a thought that seemed an interesting footnote enough for me to write down until checking on line it seemed to come up indirectly as the issue of the day.
    It helps to reread Sabines essay and some clarifications in her comments to get wider comphehension of her arguements.
    I like the distinction of mass and length and what is abstract math or physics as modeling concerns this question of the what of information.

    It is the distinct we debate between theoretical and applied science. Both in relation to views of math models or physics models as hypotheses or plausibly concrete over unity of sorts.

    If zero in a sense is rest and 1 is motion regardless of the calculus like consideration over an infinite matrix of indefinite extent but these as notations do not concretely exist then just what does it mean to erase or change, write shifts of values in Turing's sense?

    Again we come to Newton's defining continuity... consecutive, contiguous, continuous of which a chain of that contiguous to me seems more foundational.

    What then if we took more of a stance like Weyl the value of mass and not the minimum distance and duration changes?

    I know I ask this as a rather overly simple if not a dumb question, but if we assert "Planck stars " exist, how would we describe a smaller one falling into a larger one in terms of physics as passing thru "event horizons. "? Does such imaginied separation make sense in the first place?

  50. It's all Greek to me...but would this relate to string theory and alternate universes? I am not very educated on this subject but find it fascinating. And what about it all being a holographic projection coming from a blackhole/event horizon? What a fun subject to speculate about :-D

  51. The main problem is the collapse.
    I suppose it can't happen not due to some quantum reason (no known force can justify it) but due to the fact that the metric become negative below the event horizon. The physical meaning have to be looked in a change of the curvature sign and it happens due to the torsion of the space-time itself. We have a strong evidence about it: dark energy.
    In other word there's no need to look a solution to information paradox as the singularity can't be formed. From a dynamical point of view there aren't any force balances.
    My idea is that inside to any black hole exist an entire universe
    Finally I don't believe that any black hole may evaporate.


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