Wednesday, March 28, 2018

Why Black Stars Aren’t A Thing.

Not a black star,
but about equally real.
I came to physics by accident. I had studied mathematics, but the math department was broke. When I asked the mathematicians for a job, they sent me to the other side of the building. “Ask the physicists,” they said.

The physicists didn’t only give me a job. They also gave me a desk, a computer, and before I knew I had a topic for a diploma thesis. I was supposed to show that black holes don’t exist.

I didn’t know at that time, but it was my supervisor’s shtik, the black-holes-don’t-exist-speech. Prof Dr Dr hc mult Walter Greiner, who passed away two years ago, was the department head when I arrived. His argument against black holes was that “God wouldn’t separate himself from part of the universe.” Yo. He mostly worked on heavy ion physics.

I had made pretty clear to him that I wasn’t interested in heavy ion physics. Really I wasn’t sure I wanted to graduate in physics at all; it wasn’t even my major. But I was the math person, so certainly I could prove that black hole’s weren’t, no?

It was either that or computer simulations of big nuclei or back to the broke mathematicians. I picked the black holes.

That was 1997. Back then, measurements of the motion of stars around Sag A* were running, but they would not be published until 1998. And even after Sag A* proved to be dark, small, and heavy enough so that it should be a black hole, it took ten more years to demonstrate that indeed it doesn’t have hard surface, thus providing evidence for a black hole horizon.

We now know that Sag A* is a supermassive black hole, and that such black holes are commonly found in galactic centers. But when I was a student the case was not settled.

Greiner had explained to me why he thought black holes cannot form in stellar collapse. Because we know that black holes emit radiation, the famous “Hawking radiation.” So, when a star collapses it begins emitting all this radiation and it loses mass and the horizon never forms. That was his great idea. Ingenious! Why had no one thought of this before?

After some months digging in the literature, it became clear to me that it had been tried before. Not once, but several times, and equally many times it had been shown not to work. This was laid out in various publications, notably in Birrell and Davies’ textbook, but Greiner’s interest in the topic didn’t go far enough to look at this. Indeed, I soon found out that I wasn’t the first he had put on the topic, I was the third. The first delivered a wrong proof (and passed), the second left. Neither option seemed charming.

Black hole with accretion disk
and jet. Artist's impression.
[Image Source]
The argument for why Greiner’s idea doesn’t work is a shitload of math, but it comes down to a very physical reason: You can’t use Hawking radiation to prevent black holes from forming because that’s in conflict with the equivalence principle.

The equivalence principle is the main tenet of general relativity. It says that a freely falling observer should not be able to tell the presence of a gravitational field using only data from their vicinity, or “locally” as the terminology has it.

Hawking radiation obeys the equivalence principle – as it should. This means most importantly that an observer falling through the black hole horizon does not notice any radiation (or anything else that would indicate the presence of the horizon). The radiation is there, but its wavelengths are so long – of the size of the horizon itself – that the observer cannot measure the radiation locally.

If you want to know how Hawking-radiation affects the black hole you must calculate the total energy and pressure which the quantum effects creates. These are collected in what’s called the (renormalized) stress-energy-tensor. Turns out it’s tiny at the black hole horizon, and the larger the black hole, the smaller it is.

All of this is perfectly compatible with the equivalence principle. And that’s really all you need to know to conclude you can’t prevent the formation of black holes by Hawking-radiation: The contribution to the energy-density from the quantum effects is far too small, and it must be small because else an infalling observer would notice it, screwing over the equivalence principle.

What normally goes wrong when people argue that Hawking-radiation can prevent the formation of black hole horizons is that they use the result for the Hawking radiation which a distant observer would measure. Then they trace back this radiation’s energy to the black hole horizon. The result is infinitely large. That’s because if you want to emit anything at the horizon that can escape at all, you must give it an infinite amount of energy to start with. This is nonsense because Hawking radiation is not created at the black hole horizon. But it’s this infinity that has led many people to conclude that a collapsing star may be able to shed all of its energy in Hawking radiation.

But whenever you do physics and the math gives you an infinity, you should look for a mistake. Nothing physically real can be infinite. And indeed, the infinity which you get here cannot be observed. It is is cancelled by another contribution to the stress-energy which comes from the vacuum polarization. Collect all terms and you conclude, again, that the effects at the horizon are tiny. Done correctly, they do, of course, obey the equivalence principle.

In summary: Yes, black holes evaporate. But no, the energy-loss cannot prevent the formation of black hole horizons.

That was the status already in the late 1970s. Walter Greiner wasn’t the first but also not the last to try using quantum effects to get rid of the black hole horizon. I come across one or the other variation of it several times a year. Most recently it was via a piece on Science Daily, which also appeared PhysOrg, Science Alert, Gizmodo, BigThink, and eventually also Scientific American, where we read:
Black Hole Pretenders Could Really Be Bizarre Quantum Stars

New research reveals a possible mechanism allowing “black stars” and “gravastars” to exist

These articles go back to a press release from SISSA about a paper by Raúl Carballo-Rubio which was recently published in PRL (arXiv version here).

Carballo-Rubio doesn’t actually claim that black holes don’t form; instead he claims – more modestly – that “there exist new stellar configurations, and that these can be described in a surprisingly simple manner.”

These new stellar configurations, so his idea, are stabilized by strong quantum effects in a regime where general relativity alone predicts there should be nothing to prevent the collapse of matter. These “black stars” do not actually have a horizon, so the quantum effects never actually become infinitely large. But since the pressure from the quantum effects would get infinitely large if the mass were compressed into the horizon, the radius at which it stabilizes must be outside the horizon.

In other words, what stabilizes these black stars is the same effect that Greiner thought prevents black holes from forming. You can tell immediately it’s in conflict with the equivalence principle for there is nothing locally there, at the horizon or close by it, from which the matter would know when to stop collapsing. At horizon formation, the density of matter can be arbitrarily low, and the matter doesn’t know – cannot know! – anything about redshift from there to infinity. The only way this matter can know that something is supposed to happen is by using global information, ie by violating the equivalence principle.

Indeed that’s what Carballo-Rubio does, though the paper doesn’t really spell out where this assumption comes in, so let me tell you: Carballo-Rubio assumes from the onset that the system is static. This means the “quantum star” has no time-dependence whatsoever.

This absence of time-dependence is an absolutely crucial point that you are likely to miss if you don’t know what to look for, so let me emphasize: No stellar object can be truly static because this means it must have existed forever and will continue to exist for all eternity. A realistic stellar object must have formed somewhen. Static solutions do not exist other than as math.

The assumption that the system be static is hence a global assumption. It is not something that you can reach approximately, say, at the end of a collapse. Concretely the way this enters the calculation is by choice of the vacuum state.

Yes, that’s right. There isn’t only one vacuum state. There are infinitely many. And you can pick one. So which one do you pick?

Before we get there, allow me a digression. I promise it will make sense in a minute. Do you recall when Walter Wagner sued CERN because turning on the LHC might create tiny black holes that eat up earth?

It is rare for black hole physics to become a matter of lawsuits. Scientists whose research rarely attracts any attention were suddenly in the position of having to explain why these black holes, once created, would be harmless.

On the face of it, it’s not a difficult argument. These things would have interaction-probabilities far smaller than even neutrinos. They would readily pass through matter, leaving no trace. And being created in highly-energetic collisions, they’d be speedy, fly off to outer space and be gone.

But then, these tiny black holes would have a small but nonzero probability to become trapped in Earth’s gravitational field. They would then keep oscillating around the center of the planet. And if they stuck around for sufficiently long, and there were sufficiently many of them, they could grow and eventually eat up Earth inside-out. Not good.

That, however, the scientists argued, could not happen because these tiny black holes evaporate in a fraction of a second. If you believe they evaporate. And suddenly theoretical physicists had to very publicly explain why they are so sure black holes evaporate because otherwise the LHC might not be turned on and their experimentalist friends would never forgive them.

Rather unsurprisingly, there had been one-two people who had written papers about why black holes don’t evaporate. Luckily, these claims were easy to debunk. The court dismissed the lawsuit. The LHC turned on, no black holes were created, and everyone lived happily ever after.

For me the most remarkable part of this story isn’t that someone would go try to sue CERN over maybe destroying the world. Actually I have some understanding for that. Much more remarkable is that I am pretty sure everyone in the field knows it’s easy enough to find a theoretical reason for why black holes wouldn’t evaporate. All you have to do is postulate they don’t. This postulate is physical nonsense, as I will explain in a moment, so it would merely have complicated the case without altering the conclusion. Still I think it’s interesting no one even brought it up. Humm-humm.

So what’s that nonsense postulate that can keep black holes from evaporating? You choose a vacuum state in which they don’t. Yes, you can do that. Perfectly possible. It’s called the “Boulware state.” The price you pay for this, however, is that the energy created by quantum effects at the black hole horizon goes to infinity. So it’s an unphysical choice and no one ever makes it.

Ah! I hear you say. But not very loudly, so let me summarize this in plain terms.

You can assume a black hole doesn’t evaporate on the expense of getting an infinite amount of stress-energy in the horizon region. That’s an unphysical assumption. And it’s the same assumption as postulating the system does not change in time: Nothing in, nothing out.

And that – to tie together the loose ends – is exactly what Carballo-Rubio did. He doesn’t actually have a horizon, but he uses the same unphysical vacuum-state, the Boulware state. That’s the reason he gets such a large quantum pressure, hence violating the equivalence principle. It comes from the assumption that the system is static, has always been static, and will always remain static.

Let me be clear that Carballo-Rubio’s paper is (for all I can tell) mathematically sound. And the press-release is very carefully phrased and accurate. But I think he should have been clearer in pointing out that the assumption about time-independence is global and therefore he is describing a physically impossible situation that is not even approximately realistic.

If you followed my above elaborations, it should be clear that the details don’t matter all that much. The only way you can prevent a horizon from forming is to violate the equivalence principle. And worse, this violation must be possible when space-time curvature is arbitrarily small, as small or even smaller than what we have here on Earth.

Of course you can postulate whatever you want and calculate something. But please let us be clear that all these black stars and gravastars and quantum stars  and what have you require throwing out general relativity in regions where there is no local measure whatsoever that would call for such a breakdown. Doesn’t matter how much math you pour over it, it’s still in conflict with what we know about gravity.

The realistic situation is one in which matter collapses under its gravitational pull. In this case you have a different vacuum state (the Unruh state), which allows for evaporation. And that brings you full circle to the above argument for why the stress-energy is too small to prevent horizon formation. There’s no way to avoid the formation of a black hole. Nope, there isn’t. Black holes really exist.

As to my diploma. I simply wrote my thesis about something else but didn’t mention that until after the fact. I think Greiner never forgave me. A few years later he fired me, alas, unsuccessfully. But that’s a different story and shall be told another time.

That was a long post, I know. But I hope it explains why I think black stars and gravastars and qantum stars and so on are nonsense. And why I happen to know more about the topic than I ever wanted to know.


  1. Sabine,
    there are also (theoretical) objects called boson stars, where the gravitational collapse is halted by effects related to the quantum uncertainty relations. Usually they are modeled by equation like Schrodinger-Newton. I guess these objects would also qualify as "gravastars" as well. The difference seems to be that Carballo-Rubio relies on quantum vacuum effects (ie, QFT).
    On the other hand, S-N does not allow collapse. Perhaps one could generalize that to include GR effects.

  2. Fascinating story!

    A (possibly naive) question: would it be possible that black holes where all their matter is behind an event horizon exist, but that there's some even stronger force that prevents all that matter from collapsing into a (mathematical) singularity?

    It would require a force that is stronger than all known forces.

    If this is what happens happens then in theory this might be measurable via the visible diameter of the event horizon of black holes: their event horizon would be slightly larger than the predicted size from a true singularity where all matter collapses into a single point.

    It might also be measurable by finding this force independently, via even larger particle colliders?

    Does my suggestion even make sense?

  3. Hope your book is as entertaining as your blog. That was a fun read.

  4. Longtime reader, just wanted to say thanks for another great post.

  5. I.A.

    Indeed that's what most of my colleagues think what happens. The "force" in question which prevents total collapse to a singularity is pressure due to quantum gravitational effects. To be careful, it's not strictly speaking a force, but one may loosely speaking interpret it this way. This effect however only gets relevant once the curvature comes into the Planckian regime. That's far inside the horizon (unless the black hole is very small, in which case it's entirely a quantum object).

  6. Opamanfred,

    Theoretically you can invent flying pigs ;)

  7. Sabine: When the press release says black stars, are they referring to black stars proposed by Tanmay Vachaspati or something else?

  8. Shantanu,

    I don't know. I actually didn't read the articles, I just looked at the paper. I merely used the term here so readers understand the connection to the recent headlines.

  9. I think there are more issues in this area than people think, Sabine. For example, the principle of equivalence only applies to an infinitesimal region, to a region of no extent. So it doesn't apply at all. This why Synge said the midwife should be buried in his preface. I side with Oppenheimer, and Einstein. But not totally, because he didn't think in terms of a hailstone. It forms from the inside out.

  10. is it possible dark energy can resist the contraction of a black hole so that either a black hole does not form or something other than a black hole forms. and is there a higgs field inside a black hole, and does it have the same exact properties as a higgs field on flat spacetime

  11. But one has the information paradox. What I understood is that something HAS to be wrong e. g. the equivalence principle or unitarity.

    Just as layman, for me the interior solution of a Kerr black hole seems unbelievable, anyway there is no way to check it (a phisophical question is then does the interior exist at all, it is like the multiverse). Also the infinite redshift at the horizon is disturbing. It is like you could break the speed of light barrier. All this principle of complementary is difficult to swallow. I know you can get fooled by "common sense" but still.

  12. Equivalence Principle violation: Baryogenesis' Sakharov conditions demand vacuum chiral anisotropy toward hadrons. Enantiomorphs (opposite shoes) embed within chiral vacuum background (mount a left foot) with different energies. Extreme geometrically chiral-divergent test masses vacuum free fall along non-identical minimum action trajectories.

    Load U/Washington's Eötvös balance with 40 g of (DOI:10.1107/S0108767303004161) single crystal quartz test masses, space group P3(1)21 (right-handed) versus P3(2)21 (left-handed). Emergence scale is the 9-atom 0.113 nm³ unit cell, 6.68×10^22 pairs of opposite shoes. ~1 part in 20 trillion sensitivity versus ~1 part-per-billion signal.

    It violates accepted theory! It sources baryogenesis, Milgrom acceleration, the cosmological constant; ends SUSY and much of M-theory; removes parameterizations postulating exact vacuum mirror symmetry; and can arise from Einstein-Cartan gravitation. Look.

  13. Sabine, I.A. are you referring to Einstein-Cartan theory which is said to dispose of the singularity? I've never seen you write about Einstein-Cartan theory... what do you make of it?

  14. Sabine, thanks for the great post about black hole evaporation. I am not a specialist in this area and I learned a couple of new (for me at least) things from your post. It seems to me that black holes do evaporate via Hawking radiation and I agree totally with your conclusions black holes exist, Hawking radiation is consistent with the strong equivalence principle, and Hawking radiation cannot prevent black hole formation. But since the correct quantized version of General Relativity is yet to be found, is it really certain that this so-far undiscovered theory would predict black hole evaporation? Although I think it would, there are differing ideas about this. For example, Adam Helfer has doubts about it ( and other have doubts about Unruh radiation ( and the Unruh effect (, and These authors may make Carballo-Rubio type errors but I am not expertise enough in this area to judge. So any thoughts you have on these are much appreciated and I would very much appreciate your thoughts on ( as a possible solution to the so-called black hole information paradox.

  15. "Nothing physically real can be infinite." Ok I do happen to believe this for reasons well argued by Unger & Smolin. But it is still common to hear physicists claim that, or insist on a *singularity* at the center of black holes. Doesn't (or wouldn't) this blatantly violate the "no physical infinities" hypothesis?

  16. Didn’t Hawking himself write a paper a few years ago asserting that black holes can’t really form? There is a real issue with time from the perspective of the infalling observer - at the horizon time relative to infinity has slowed to zero, so the part inside the horizon in some sense doesn’t happen according to the timeline of the external observer. So what’s really going on there?

  17. An interesting article, Sabine, and while I don't doubt for an instance that Black Holes exist, and while I don't know much about them, I would have thought it is still an assumption that the equivalence principle holds at the event horizon. I am thinking that Einstein's relativity is really only significant at extreme velocities or extreme gravitational field strength, but is it not possible that the equivalence principle could fail there too, or at least need modification?

  18. Thank you for your enlightening comments, Dr. B. I had lots of questions about Carballo-Rubio's work, and you've now set my mind at ease.

    I brought up the 'black star' issue at a recent Caltech astrophysics lecture and was met with blank stares. Finally, a brave post-grad ventured the idea that until a reliable equation of state for neutron stars is developed, the never-never land between a semi-stable, super-dense NS and a black hole will remain elusive.

    (By the way, as a grad student our QM professor decided to use Greiner's texts as the primary textbooks, later admitting it was a huge mistake.)

  19. johnduffield,

    You have a fundamental misunderstanding there. The eq principle applies approximately on scales below the curvature radius. Besides, it's rather idiotic to say it doesn't apply at all, given that it's been experimentally shown to apply to excellent precision.

  20. Sea stories by Sabine, 'colorful' language & aIl."


    Re: physically real, infinities

    Black hole singularity density??

  21. neo,

    Dark energy is a long-distance effect, not a short-distance effect. You can still form black holes in a space with dark energy. They still have a horizon; they still have a singularity.

  22. opamanfred,

    When I said "you can" I didn't mean you in person, but I used it in the sense of "one can". The paper you mention is about something entirely different. They look at "stars" made up of a different kind of *matter*. So that matter will build pressure differently from what normal matter does, leading to different branches of stability. That's all well and fine, leaving aside that I don't think these things exist. The stuff that I am discussing here are objects made of *normal matter* that is (supposedly) stabilized or prevented from collapsing by some unusual quantum effects.

  23. Louis,

    Yes, Helfer was one the guys. I looked at his papers 10 years ago and back then I might have been able to tell you what's going wrong. I hope you will understand that I don't have the time to read and comment on each of the papers you list.

  24. Bill,

    Kudos to the brave student, but the NS eos has very little to do with the argument. There's an upper limit to the possible mass of NS that's almost independent on the eos, it's somewhere close by two solar masses. The effect Carballo is after should kick in no matter what and stabilize the thing. Best,


  25. APEppink,

    Don't know what you mean. Maybe try to express yourself clearer.

  26. Farid,

    Well then it seems you misunderstood that.

  27. Matthew,

    I don't know anyone who thinks an observable that reaches an infinite value is a real thing. Instead, it's generally assumed to be a mathematical artifact that signals a breakdown of the theory.

    1. Hi Sabine.. are you implying that because the interior of a black hole is unobservable a "real infinity" might lurk there?


    The best argument that the LHC is mostly harmless is that even higher-energetic collisions occur regularly in the atmosphere, due to cosmic rays.

    What about tidal forces? Are they not locally measurable? This formulation of the equivalence principle, which is text book standard, you are quite forgiven, continues to puzzle me.

  30. John,

    No, they are not, they're curvature contributions. Second derivatives of metric. First derivative is the gradient, second is the tidal force. Geodesic deviation is basically the same thing.

  31. Sabine,

    I know all that stuff mathematically, i.e., that tidal forces are related to geodesic deviation, which is related to the Riemann tensor, which is related to curvature - basically §11.2 of the classic by Misner, Thorne, and Wheeler. But that is not my point.

    Why can such quantities not be obtained locally, i.e., in the vicinity of some freeling falling observer? Is it not possible, at least in principle, or as a thought experiment, to study the trajectories of test particles in the limit of vanishing displacement vectors (between pairs of geodesics), and from this extract information about tidal forces?

  32. John,

    I think this is a terminology issue. When we say "not locally" that's what we mean: They're curvature contributions (or even higher order). Ie, you have to be able to measure curvature to tell gravity apart from acceleration. What this expression tells you is the order of magnitude of the expected effect: the smaller the curvature, the smaller the effect. (On a similar note, higher order derivative theories are sometimes referred to as non-local though I think it's terribly misleading.)

    Whether or not you actually can measure them depends on how precisely you can measure what. There are a lot of thought experiments about what Alice can and cannot measure how and with what detector when she falls through the black hole horizon. One could spend decades discussing those, but the upshot is what I told you above.

  33. "Matthew,


    2:36 AM, March 29, 2018"


    Just trying to get a handle on what you think is the case re infinities. Matter sucked into black holes is crunched to infinite densities at singularities, at which point it's hypothesized(?) 'conventional' physical law breaks down. What is happening there then? Really. Physically. Or is that the Big Question?

    I admire your devotion in replying to so many of these comments, of varying quality. Where you find the time, l can't imagine.

    Thank you.

  34. Sabine,

    I think I agree concerning the terminology issue. But then I think the equivalence principle should rather be stated somewhat along the following lines: "The part of the gravitational field that is purely inertial can always be (locally) transformed away."

    But perhaps such a statement is physically vacuous in the sense of being essentially just a mathematical statement: that, apart from pathological cases, I suppose, it is always possible to locally transform the metric to Minkowskian form, and to transform away the Christoffel symbols (because there are the same number, forty, of them as there are first-order derivatives of the metric.)

  35. Addition to my former post: Or, coming to think of it, perhaps not: The physics enters, I guess, through the geodesic equation (which becomes for vanishing Christoffel symbols a statement of Newton's first law).

  36. APEppink,

    GR breaks down when the curvature (or higher invariants) reaches the Planckian regime, ie before the singularity is formed. That's when quantum effects of gravity become important. Yes, what happens then is the big question.

  37. John,

    What you say is basically correct but you have it backwards. The equivalence principle is what leads you to use tensor calculus on Riemannian manifolds in the first place. The latter is a more mathematical version of the former. Once you have the latter the former is basically implied. (That's leaving aside that some people claim if you have additional long range interactions these violate the equivalence principle which I think is more confusing terminology.) As an aside, this is also why it's so hard to change anything about GR. Best,


  38. Equivalence Principle violation? Euclid's incomplete Fifth Postulate cannot be falsified by rigorous derivation. One cannot derive a suitable EP test from accepted theory.

    1.74 solar-mass 465.1 Hz PSR J1903+0327 (neutron star) and a 1.05 solar-mass star are a 95.17-day binary. -15.3% gravitational binding energy (>100 MeV/nucleon) vs. -0.000424% (3.73 keV/nucleon); 1.8×10^11 vs. 30 surface gees; 2×10^8 vs. 5 gauss magnetic fields; twice nuclear density superconductive protons and superfluid neutrons versus atomic 11.8:1 H:He atomic abundance plasma; extreme isospin and lepton number divergences; and pulsar 11% lightspeed equatorial spin validate the Equivalence Principle for orbit, periastron precession, and gravitational radiation orbital decay.

    Black hole and neutron star mergers are exactly described by general relativity. Zero external field spin dipoles (orbital versus spin electron angular momenta as ferrimagnets or composite test masses) Eötvös balance give null outputs.

    Test spacetime geometry with geometry. The smallest geometrically chiral mass emergent scale is atomic bonding of light atoms, less than 0.2 nm³ as a periodic crystal or a multiple homochiral center organic molecule. Look - in chemistry, not in physics.

  39. does the dark energy act as an anti-gravity effect inside a black hole, resisting further contraction?

  40. Could I safely say this ?

    The evidence of Hawking radiation is not yet verified by experiments (too hard to observe, it can be calculated, Hawking temperature is even lower than 3k, the CMB) , but this idea has been accepted by almost of all physicists.


  41. So what about the black hole firewall that has been postulated? It would seem to violate the equivalence principle.

  42. Sabine - thanks for the link, I remember reading your comments back then, they were very helpful.
    However, my point was more that, the perspective of the infalling observer is not valid beyond the event horizon, and assuming it’s only an apparent horizon that will disappear given long enough external time, the infalling observer never actually hits it at all. All these equivalence principle arguments depend on the perspective of that infalling observer, but if their time never reaches the point of crossing the horizon, then the argument doesn’t really tell you anything.

  43. Thanks for this. I changed my mind on the whole Trans-Planckian problem after I looked into it. Had to read the post and the Giddings paper to really get all of it.

    I think Einstein is right - the equivalence principle rocks.

  44. Always enjoyed Greiner's textbooks. Disappointing to learn that he was so petty.

  45. Yes one needs a privileged frame to argue that some kind of new physics is locally expected when one gets close to the horizon. May be when the potential in this privileged frame reaches some threshold. Why should we dismiss such possibility which indeed implies equivalence principle violations. My prefered option is that GR is only valid piecewise , within finite spatial domains, and must be supplemented by new kind of laws to match (completely or not) the solutions at the frontier between various spatial domains. Why not such kind of frontier and the related new physics effects (to hopefully avoid a true horizon ) in the vicinity of the schwarzshild radius?

  46. Tom Andersen, you are right; EP is one of the most fundamental principles.

    If we consider the equivalence principle is valid everywhere, we can see that inertial and gravitational effect on some event in singular point of spacetime depends on the whole universe in principal. There are no particles as separate "balls".

    Hence the Mach effect -like interactions seem to prevent any event horizon being nothing else but an asymptote.

  47. @Tom Andersen I think Einstein is right - the equivalence principle rocks. Baryogenesis happened (Sakharov conditions, despite accepted theory). The Equivalence Principle (EP) is then violated by enantiomeric atomic mass configurations.

    One hour in a microwave spectrometer advertising 40,000:1 signal to noise ratio validates. The 1986 spectral exemplar is DOI:10.1515/zna-1986-1107. The 2018 spectrometer is; the optimized test molecule is 3:1 R:S right-handed:left-handed enantiomer pair

    van der Waals volume 0.158 nm³
    van der Waals surface area 0.234 nm²
    DOI:10.2174/138527212804004508, DOI:10.1016/S0040-4020(98)00211-7

    NOTHING in accepted theory is empirically fertile. The worst this can do is succeed. Physics is an arrogant coward for not looking. Look.

  48. I enjoyed the article, it expanding my understanding and knowledge, and that is always satisfying.

    You said something important that I think is not always recognized, "Static solutions do not exist other than as math". Because we can imagine physical things statically they can appear to exist in such a state and it may even seem intuitive, yet scientifically wrong. I think if more people keep that in mind it could help their scientific understanding. I know it has helped me understand many things, including spacetime a bit better.

  49. Matthew,

    No. What I am saying is that in GR, there is a "real" singularity in the black hole, but since the theory breaks down before that happens, nobody thinks the singularity is real.

  50. I learned something important : "Hawking radiation is not created at the black hole horizon."
    But may be the Hawking radiation still needs the existence of a genuine horizon ... otherwise the argument "Because of the absence of an event horizon, the QBH (Quasi Black Hole : gravastar) does not emit Hawking
    radiation." at page 3 of is wrong ?

    Do you confirm it's wrong ?
    Notice my question is not about the validity of the gravastar model.

  51. Do not mean to push you Sabine but I read more than a few cosmologists who claim that there is a "real" singularity at the center of a black hole and do not otherwise qualify that belief. To be clear I agree with you, so no need to respond. Merely pointing out that not everyone denies the singularity is real.

  52. Uncle Al,

    All EP-violations can be explained by our lack of knowledge of initial conditions. For instance it doesn't make any sense to mess up with classic point mass setup and statistics of quantum mechanism.

  53. Frederic,

    Depends on what you mean with "wrong." As I explained in this blogpost, you can just assume this to be so. There is nothing mathematically wrong with that. It's "just" physical nonsense because it violates the equivalence principle.

  54. Matthew,

    Well I didn't make a poll, but I don't know anyone who thinks the singularity is real. I am surprised you claim you know some. Do you happen to have a reference?

  55. @Eusa " All EP-violations can be explained by our lack of knowledge of initial conditions" The EP locally (re curvature, etc.) requires test masses vacuum free fall along identical minimum action trajectories. The EP fails for divergent spacetime embedding energies. I enumerated above: no measurable observable - classical, relativistic, quantum mechanical; composition, field, spin, orbit - of any divergence magnitude violates GR prediction.

    Spacetime geometry itself is untested, GR versus Einstein-Cartan. Massless boson photons detect no vacuum refraction, dispersion, dissipation, dichroism, or gyrotropy. However, baryogenesis discriminates massed fermion hadrons (quarks) - no prior observation constraints. Roughly equidimensional ~0.200 nm³ molecular volumes are local. Geometric chirality can be observed and calculated but not measured. Chiroptical measures do not couple to mass distribution. X-ray (Flack parameter) and microwave measures are crossed fields.

  56. @Uncle Al,

    Our debate is under the threat to deepen to the level out of the publishing policy of the thread...

    Shortly. I think Einstein converted the energy of gravitational field as a part of the "observed appropriate masses of heavenly bodies" for objects. The right solution could be such that the whole mass must be integrated from the gravitational field of particles. Then all initial conditions will be taken into account from "trajectory to eternity" and all local quantum fluctuations are indentified as their statistical status.

  57. Ironic that Greiner didn't like event horizons. One of his intuitions was the vacuum "spark" that would occur if you had a naked charge of Z>127: the electric potential becomes comparable to the mass of an electron over the electron's wavelength. The vacuum rips apart a virtual e+e- pair and spits out an e+, reducing the offending charge.

    I have always understood Hawking radiation to follow essentially the same physics. If you have a region of space stressed by a gravitational gradient it rips apart a pair of photons and spits one out, leaving behind a reduced the gravitational charge.

    This is where I think the eqivalence principle fails in the face of quantum mechanics. An accelerating elevator will never produce photons from the vacuum because there is no field gradient. Yes it is all very well to argue the principle is limited to infinitesimal regions but this is essentially refusing to take the derivative. Nevertheless the physics is different if you have virtual particles present. I don't see this as a problem since GR is purely classical, but when you add QM what's the problem with abandoning the equivalence principle?

    I look forward to the story of the firing...

  58. There's a 'real' singularity inmidst the BH 'cause GRT is not able to describe quantum gravity. For me, beeing an very interested layman and not a physicist, a 'real' singularity with infinit density and zero volume seems to be as unreal (mention: I did NOT write 'unnatural'...) and absurd, as Calabi-Yau spaces, the spring landscape or eternal inflation (maybe inflation in general...). I always ponder, wheather a good portion of common sense would help to separate the weird ideas from the good (mention: I did NOT write 'natural'...) ones - but on the other hand, where's commom sense when it comes to the physical facts like the double slit experiment, the cosmic background or quantum teleportation...? Hrrumpppf...

  59. Ok, so to be clear they don't say "...and the singularity is a real physical infinity", they just don't qualify "singularity at center of black hole". I once asked Ethan Siegal about this specifically and he said "I'm not sure".

  60. Matthew,

    Two things. First, some people don't like to say that the singularity is at the center of the black hole, not because of the singularity but because of the word "center" (one can debate whether that's a meaningful term). Second, leaving aside the issue of what's the center of a black hole, there's nothing uncertain about whether GR does have a singularity inside the black hole. It does. It's just that, as I said, no one thinks it's physically real. At least no one I know.

  61. Uli,

    As I said that's what everyone thinks. I don't know, though, what makes you draw a connection between curvature singularities in GR and the string landscape. "Common sense" is, by and large, a bad guide to scientific understanding.

  62. Ok, not the center, just unqualified "singularity in a black hole". Comes out to same thing. Only you and Unger/Smolin (that I have seen) are explicit in saying that what ever it is, it cannot be literally infinite

  63. Matthew,

    As I've now iterated like a dozen times, almost everyone who works in the field agrees on this.

  64. Dr. Hossenfelder -- a tangentially related question.

    It seems obvious at this point that mass has been dumping energy into spacetime in the form of gravitational waves since the universe's birth. Has anyone looked into a relationship between that energy and the accelerating expansion of the universe ("dark energy" effects)?

    I hesitate to ask, as I'm guessing someone's thought of it, done the math, and dismissed it. I'm just curious.

  65. Sabine,

    I agree with your statement about a free-falling observer not perceiving Hawking radiation due to the equivalence principle (who wouldn't) but the collapse scenario proposed in arxiv:0712.1130, arxiv:1409.1501 and several other papers in which Raúl himself has participated takes into account this fact. The article Black Stars, Not Holes (10.1038/scientificamerican1009-38) talks briefly about their proposal and has a section about vacuum polarization and how it exerts a repulsive force if matter's fall is slowed. If I remember correctly, it occurs due to Unruh radiation deviating the trajectory of the infalling matter from free-fall and that's when Harking radiation begins to "appear".

  66. Jonathan,

    Gravitational waves are not dark energy. Dark energy is a type of energy which you cannot get from normal matter or radiation.

  67. Julio,

    Yes, you can look at it the other way round and assume that the fall is slowed, but that just brings up the question why would that be if the equivalence principle, etc etc. In any case, to repeat it once again, I do not question even for a moment that you can write down a mathematically consistent theory that does that for you. I just think it's physical nonsense. Wake me up if someone sees these things.

  68. Sabine, your post is absolutely fantastic! Thank you for dumbing the matter down to an educated lay audience, like myself! Where do I sign to have you as my mentor? (not a Ph.D. mentor as I already have a Ph.D.) I am talking about a mentor for "out-of-the-box thinkers, the ancient philosophers type of mentor); after all isn't that the meaning of Ph.D.?!

    Finding a genius is rare. Finding one that can speak to "human beings" is a once-in-a-lifetime deal, but finding one that is also uncurby is a quasi-impossible triad!

    Thank you Sabine.

  69. Doesn't Unruh radiation also violate the equivalence principle, since it can only be observed by a kinematicly accelerated observer, but not by an observer at rest in a gravitational field, which should be locally equivalent to kinematic acceleration? If you accelerate with 1g the Rindler horizon would be in a distance of 1 lightyear, but if you are at rest on the surface of the earth you can see infinitely far.

  70. Yukterez,

    You can see Unruh radiation in a gravitational field, but in this case it's called "Hawking radiation". The two are not exactly the same b/c Unruh radiation isn't normally computed for a spherically symmetric case. Also, neither of the two has actually been measured, as you probably know. Best,



    Solve this problem first. An electrically charged ball on my desk does not radiate. Does this violate the equivalence principle? Could one use the presence or absence of radiation to decide whether one is at rest in a gravitational field or being uniformly accelerated? (I know the answer, but it is an interesting puzzle.)

  72. So if you stand at rest on the surface of the earth you would also receive Unruh radiation (of approximately 1 ly wavelength), not only if there is a horizon beneath you? But the earth does not evaporate, so where would the energy come from?

  73. Yukterez,

    It's the gravitational field that creates the radiation, not the horizon. The horizon is merely the reason why the radiation is not pure. A time-independent system can't evaporate, but that's tautologically true. Best,


  74. @ Phillip Helbig: the charge at rest in the gravitational field should not radiate in the frame of an observer which is also at rest in the gravitational field, but it should radiate in the frame of a free falling observer. In this scenario the free falling observer should pay for the radiation he receives by accelerating slower than he would in the absence of the charge. Then the energy of the radiation is accounted for by the kinetic energy of the free falling obverser relative to the charge at rest. In the case of a black hole it is believed that the black hole itself pays for the radiation with it's own mass. But if you stand at rest on the surface of the earth and the earth does not evaporate I don't understand who pays for the radiation, since you do not have kinetic energy relative to the earth which you could lose in order to pay for the radiation. So is it the vacuum itself that pays for the Unruh radiation received by a stationary observer?



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