A week ago, we discussed the media buzz about Hawking's claims that event horizons don't exist.

In the following days, I've read numerous reactions of physics bloggers (in the blogosphere) and other physicists (in the e-mail). While I agreed with many detailed statements and much of the spirit of some people's reactions, there are still too many things that I disagree with; many things they haven't said; many things that seem orthogonal to things that matter; many confusions they still have about the actual way how black holes work, and so on.

There is clearly nothing such as a "broader quantum black hole community" that would live similar intellectual lives and evaluate the events and discoveries in a comparable way.

Here, I wanted to discuss some points in the replies by

Matt Strassler, Clifford Johnson, and Sabine Hossenfelderas well as some extra comments by some of my e-mail correspondents who will remain anonymous (at least for a while).

Well, first, it may be a good idea to summarize what I think that has happened.

Stephen Hawking may be considered the founder – or one of two founders with Jacob Bekenstein – of the quantum or microscopic research of black hole physics. Hawking's papers deriving his radiation were remarkably explicit, seemingly waterproof, and they also implied that the information was apparently lost. Two decades later, it became pretty clear due to novel research – especially stringy research and especially AdS/CFT (and perhaps Matrix theory) within this research – that this conclusion had to be just an artifact of approximations and Hawking himself agreed that the information was preserved in the exact theory when he surrendered in a bet against John Preskill.

Hawking had been incorrectly predicted to enjoy the last months of his life almost 40 years ago – further indicating that medicine isn't quite at the same level of precision and reliability as physics, something he must be doubly happy about. Given the obvious physical difficulties I can see, the degree of Hawking's contact with the new developments in physics research has seemed remarkable to me. Many relatively recent papers he wrote or co-wrote were very valuable and often correct and new.

Even in the fuzzball insanity that erupted in Summer 2012, Hawking looked remarkably sane. Now, he wrote the two-page paper with no equations, with some buzzwords that are very close to the vocabulary of the smartest and most reasonable quantum black hole researchers of the current era, and with some bold propositions that admit some flexibility in their interpretations.

*The diagram is very different if you turn it upside down. Is that a problem?*

I am confident that Hawking incorrectly believes that due to the massive CPT-asymmetry we see in all realistic black hole causal diagrams, the existence of these diagrams and especially the event horizons contradicts the CPT theorem, so the horizons cannot exist even as an approximation. All other bloggers completely ignore this CPT issue even though it's clearly meant to be the main argument in the short paper; I wonder whether anyone among them has read the whole short paper at all.

**Why Hawking is saying a bold and wrong thing**

The formation of the black hole is very fast, the evaporation is very slow, and the Penrose causal diagram looks completely different if we turn it upside down. There are no processes that look like upside-down-rotated causal diagram for a black hole, Hawking notices, so the laws that allow for such diagrams must violate the time-reversal symmetry or, more precisely, the CPT theorem. He "rules out" the event horizons as well as the black hole remnants and firewalls (the last two chaps deserve to be eliminated but for other reasons).

That may sound reasonable to Hawking but it is nothing else than a misunderstanding of the character of irreversibility in the real world. The phenomena in the real world are irreversible because the entropy increases. This means that the time-reverted processes are actually possible; they are just exponentially i.e. insanely unlikely. The ashes coming from a coal-burning furnace rarely look like a perfectly healthy Bible although it's possible in principle and many believers in Jesus' miracles would be inclined to vastly overestimate the probability \(\approx \exp(-10^{26})\) that the Holy Scripture may be produced in this way.

Now, the black hole formation and evaporation are among the "most irreversible processes in the Universe". What do I mean by the "degree of irreversibility"? Well, I simply quantify the degree by the amount of entropy that is being created. Black holes carry the largest entropy that can be squeezed to a given volume or that can be carried by an isolated or bound piece of matter of a fixed mass. So when they're produced from a relatively low-entropy star, the entropy increase is spectacular, and that's why the time-reverted process will look so fantastically different from the process in the right direction.

It's the whole story. Event horizons do exist as long as geometry may be talked about in the classical language at all (I will clarify this assertion later) and they violate neither CPT nor the time-reversal symmetry. So even though Hawking uses many words that could be right, I think that he does deny event horizons even as an approximation and such a denial is simply wrong.

**The truth about the event horizon**

The truth is that as long as you admit that the spacetime geometry – approximated by a classical geometry – exists at all (e.g. because you want to talk about it), then the event horizons must exist, too. This is guaranteed by some of the singularity theorems that Hawking helped to co-develop. There exist points (inside the black hole) whose whole future light cone ends in the future singularity, so there's no way – not even using light – to escape from those places to the free outer space (to scri plus i.e. \(\mathscr{I}^+\)).

Now, it's important to realize what the event horizon actually is. The Wikipedia definition is actually just fine. It's the boundary of the region [the interior BH region] composed of points whose future-directed timelike or lightlike trajectories never lead to the scri plus i.e. \(\mathscr{I}^+\), the future null infinity. On the picture above, the red triangle is the black hole interior and the diagonal lower-right boundary is the event horizon. That's because if you draw any future-directed (upward in the picture) timelike or null trajectory from a red point, it will always hit the singularity (the horizontal line with the teeth) and it will never get to scri plus i.e. \(\mathscr{I}^+\) – the whole diagonal line in the upper right corner labeled as "infinite future".

So that's why these diagrams inevitably contain event horizons. If you solve classical GR and its Einstein's equations, you simply get a geometry whose Penrose causal diagram looks like this (I included the part with the Hawking radiation, too: the radiation's effect on the spacetime geometry does not remove the event horizon). It's important to realize that a vast majority of the picture contains low-curvature, nearly flat regions where the effects of quantum gravity should be nearly negligible. Only the vicinity of the singularity (the horizontal teeth near the top) may be revised by corrections from quantum gravity. But we might just eliminate the trajectories that get close to this region, anyway, because the curvature is extremely high over there and deadly.

My point is that quantum gravity cannot really eliminate the existence of event horizons as an approximate concept that is defined relatively to some classical geometry. Everyone claiming otherwise is just wrong. Everyone claiming otherwise is in a full-fledged denial of general relativity in the regime where it should hold.

Now, we know that the information ultimately gets "from" the black hole interior because it is not lost. But we have just proven that this escaping information cannot have the form of some particles moving on a trajectory through the classical background according to its usual causal restrictions (timelike or null trajectories). Instead, the information gets out if it "tunnels" and refuses to obey the causal restrictions, the very basic consequences of a classical or near-classical Minkowskian geometry. Perhaps the information cannot be connected with any particular "places" as it is escaping the black hole interior. But a quantum (for flat spaces small) modification of the trajectories that would keep them smooth but allow the light rays to escape from the black hole interior along "smooth causally OK paths" is just impossible simply because quantum mechanics doesn't have a significant impact on the smooth regions.

In contradiction with the anonymous e-mail correspondent, I don't believe that someone is defining the black hole horizon in a vastly different way, a way that would imply that the colorful diagram above doesn't have an event horizon. It clearly does have one; it is the boundary of the region from which no one can escape along time-like or null future-directed trajectories. It agrees with the totally OK popular presentations talking about a place such that no rocket, not even an arbitrarily strong one, can allow you to escape from the black hole interior. Every good layman knows that the fastest rocket may have an arbitrarily high acceleration and de facto reach the speed of light. If this rocket can't escape, it really means that the light probably can't escape, either. That's why the black hole looks black; it classically emits no light.

**The event horizon is the most important one among horizons**

Now, I am observing this "movement against event horizons" at many places and I think it is totally misguided. My anonymous e-mail correspondent, Sabine Hossenfelder, and others would like to propose that what really matters is another surface near the event horizon that is defined differently, especially the "apparent horizon" and sometimes the "approximate Killing horizon" and "trapping horizon". These "other horizons" are defined differently and these definitions are "local" which is a feature that the physicists apparently consider an advantage.

But I think that theirs is a complete misunderstanding of the logic of the quantum-gravitational analyses of the information loss issues. The event horizon is the only "species of the horizons" that really matters for the loss of the information exactly because it's global in character. Its being global is also linked to its definition being rooted in the long-distance physics, and long-distance physics is the regime where classical general relativity – the theory apparently implying the information loss – may be trusted.

Classical general relativity leads you to make concepts as local as possible (which is why the "local horizons" may be so attractive to people who are paying too much "ideological" attention to classical GR); but the same local way of thinking is also the very reason why Hawking concluded that the information had to be lost. If you switch to a local definition of the horizon, you will throw the quantum baby out with the bath water. The "local horizons" have nothing to do with the question whether the information may get out or not and if you build your physical theory around these local concepts and at the end, if you ask about the real event horizons (a global property), you will find out that the information has to be lost. Moreover, the local horizons' precise location defines on fine, short-distance behavior of the geometry. Because quantum mechanics adds the frantic variation of the geometry everywhere, you could argue that the precise location of the "local horizons" could be "nearly everywhere" because quantum fluctuations may always locally "imitate" what's happening at other small regions anywhere else in the Universe!

So I find it obvious that all the papers (and e-mails) that completely refuse to discuss the event horizons can't possibly have anything meaningful to say about the information loss or preservation and all this movement attempting to redirect the focus on the "local horizon" is one huge misconception. As long as the objects and phenomena may be approximately described as objects and phenomena occurring in an approximately classical spacetime, it is unquestionable that this approximately classical spacetime will contain (event) horizons whenever a star-like object collapses into something we would call black holes. This is why the solution to the information loss problems was hard: one really has to abandon the idea of the classical spacetime and phenomena obeying its causal structure.

The Hawking quanta carry the information about the black hole microstate away. They contain photons. But the point is that it is practically – and to a large extent also theoretically – impossible to identify these Hawking photons with some photons emitted from a spaceship inside the black hole. So the black hole isn't quite black, it radiates, but the radiation isn't the same radiation as the radiation emitted by desperate infalling observers! Even if we decided that the photons "are the same" according to some dictionary (which would be very strange because e.g. the number of photons in the Hawking radiation has no reason to agree with the number of photons emitted by an infalling spaceship), the dictionary is very contrived and the "single photon's" path through the spacetime looks nothing like a trajectory in a nearly classical spacetime!

I think that to a large extent, all the bloggers and the younger e-mail correspondents are completely missing these points. Some of them may be writing papers but these papers don't correctly reproduce "what is really the problem" with the information loss, so they can't solve it, either. Switching from the event horizon to "local horizons" means to make all the reasoning unreliable (because it is affected by omnipresent quantum fluctuations) and to disconnect all the conclusions from global questions such as the conservation of the information.

Let me add a few paragraphs discussing the bloggers' reactions.

**Matt Strassler: Hawking wouldn't say a crazy thing**

To summarize, Matt says that a two-page paper without equations can't qualify as a "theory" and that Hawking isn't saying any "clearly wrong things", anyway, which is why the media buzz is misleading.

Well, I agree that the media buzz is almost always misleading and in this case, it has misleading aspects as well. But I think that in this case, the media buzz correctly reproduces what Hawking is saying.

Moreover, I sort of disagreed with the formal requirement that a credible "paper with a theory" has to contain equations. Of course that I think pretty much the same about the papers that avoid equations, seemingly at any cost. They rarely contain something important and so on. On the other hand, I think – and Matt has sort of agreed – that it is possible to express some mathematically sound results in a verbal language. In the 1970s, people would say that Hawking could calculate path integrals in his head. If you just imagine that he can still do such things, it's plausible that he "calculates" all the important things and arguments in his head and dictates the verbal conclusions coming from his calculations which may be more convenient than typing in \(\rm\LaTeX\).

I have no idea how I would be typing \(\rm\LaTeX\) if I could only move a tip of a finger, or whatever it is, or how I would make sure that the assistants are not typing junk \(\rm\LaTeX\). I've had lots of trouble with my laptop's keys AFCN not responding well at random moments (I've been using an external USB keyboard for weeks – I should have bought one immediately with the laptop – and I don't plan to ask anyone to fix the keyboard because the risks arguably exceed the benefits). And it's plausible that Hawking's physical limitations are even more severe than my hassle with the keyboards. ;-) Sorry, I had to present it as a joke of a dark sort because I think that Matt seemed to be completely missing all these "special circumstances" that may lead a sensible person to evaluate Hawking's density of equations a little bit differently.

More materially, I think that Matt is wrong when he says that the media misinterpret Hawking's assertions when they say that the "black holes don't exist". Hawking is explicitly saying that the "event horizons don't exist" and the only sufficiently general definition of a black hole I am aware of is the definition that it's an object that contains the "interior" from which it is impossible to causally escape. So not even fastest rockets can escape; that's pretty much equivalent to "not even light can escape". Hawking's new paper explicitly says that he believes that there are no regions from which "not even light can escape".

Matt is interpreting these things differently. He thinks that Hawking is still saying that there may be "de facto black holes" from which light can escape but no "extremely fast, accelerating rockets" can escape from those "de facto black holes". Well, I don't believe that Hawking is saying such a "mixed thing"; and I don't believe that such a "mixed thing" is defensible, either. It is pretty much impossible to construct spacetimes such that "extremely accelerating rockets" remain confined to the interior while light can get out. The reason is that "extremely accelerating rockets" approach the light-like directions almost immediately, so there is no substantial difference between fast rockets' time-like trajectories and the light rays' light-like trajectories (on a causal diagram, for example). So I think that Hawking would be silly to choose this "middle answer" and I also think that Matt is silly if he is actually and clearly choosing this "middle answer" because it seems geometrically impossible.

As far as I can say, and I have read Hawking's latest paper and other papers by the same author, Hawking is saying that even approximate event horizons don't exist; even for a good enough rocket, it's possible to escape from any region in the spacetime. Good enough rockets can't ever get confined. I believe he is saying so because he thinks that the causal limitations (for light or even for fast enough rockets) contradict the CPT theorem according to Hawking. And I have explained why Hawking is wrong and the contradiction is not there.

So even though it may be a coincidence, I think that the media's main message does reflect correctly what Hawking is actually saying. He is effectively saying that black holes don't exist, like George Chapline did. Hawking's precise imagined nature of the phenomena that occur in "objects we once thought to be black holes" is probably very different from Chapline's but the final conclusion is the same.

I feel that Matt Strassler is trying to defend some "spirit of consensus" among the serious scientists, or something like that. That's what I am reading between the lines. He says "all of us really agree and Hawking isn't saying anything that other QG folks would consider stupid". Except that I think that Hawking

*is*saying something that others consider stupid and he is not the only one. So any idea about some "consensus" is unfortunately bogus. I think that some decade ago, people were reasonable but since that time, wild life became popular in the quantum gravity research and most of the things said by sometimes pretty famous personalities that attempt to be ambitious are just incredibly stupid.

The firewalls were the latest example but there have been worse things a few years earlier, e.g. "entropic gravity" by Erik Verlinde. These insanities began to spread like an infectious disease so people's disputes about the very existence of black holes or any other basic insight is something you should be prepared for. People never get "punished" in any way for switching to the production of silly things – quite on the contrary, some of them have received millions of dollars or more precisely euros (I mean Dutch euros, to be more specific) – so there is a huge incentive to publish increasingly "provocative" things regardless of the validity which mostly means "completely wrong things". It shouldn't be surprising that if the validity of and the traditional quality standards for the papers become secondary in the "culture", the papers that are extraordinary in completely different respects inevitably proliferate.

**Clifford Johnson: Hawking vs Mathur**

Clifford says that it's sad that Hawking gets so much credit because what he's saying is just a less specific version of Samir Mathur's fuzzballs that have been around for a decade (and perhaps related insights). Well, I surely do agree with the point in general: the media often attribute some insights to some random (usually famous or friendly with them) person while the actual discoverer is often forgotten.

And I even agree with Clifford that Hawking's comments about "meteorology and chaos near the collapsing star" may sound as a poetic description of the fuzzballs. Note that fuzzballs have appeared in tons of TRF articles including Samir Mathur's guest blog. Samir and some collaborators found some BPS solution with "lots of internal hair" (like the information about the shape of a string in space). These are interpreted as the black hole microstates. The individual microstates don't have any event horizons and they're chaotic. The event horizons as we know them must come from some averaging over many fuzzball microstates. Except that I think that the way in which this common physics of GR near the horizon emerges from the (extremely interesting) fuzzball solutions is something that doesn't really follow from the fuzzball maths at all, so it's added as an "independent philosophy" supported by the authority of Samir who has "also found the fuzzballs". Because his views on other conceptual black hole questions are independent from the maths of the black hole solutions, we might say he is guessing, and that's also why we shouldn't be surprised that about 1/2 of his other statements seem right and the rest is probably wrong.

At any rate, I find the fuzzball concept and its generalizations fascinating because quite explicit, field-theoretical-like description of the individual microstates may be offered and the entropy often seems to be right. It's at least another dual description or parameterization of the black hole Hilbert spaces – but this dual description may be very inappropriate to decide what an actual macroscopic observer feels when she falls through the event horizon (if anything, or if anything specific).

If you thought that Hawking is describing the qualitative picture of Mathur's fuzzballs, I think you would be right to say that the press has misattributed this advance to Hawking and it's wrong. Well, I don't share the basic assumption: I think that Hawking is saying something much more wrong (unlike Mathur, he must now believe that the event horizons don't emerge, even after the averaging) than the wrongest things that Samir could have ever written, so I find it silly to argue who is the first originator of these wrong things. Their actual scientific value is extremely low, anyway. From my viewpoint, the media's inability to reasonably evaluate what is right and what is wrong is a worse problem than their occasional (or frequent) misattribution of particular philosophies or insights to the "wrong men".

Moreover, I don't think that Clifford is right to describe Hawking as a "newcomer". Hawking has written lots of papers – even after his most famous ones – about the conceptual black hole issues, including the information loss paradox. It's almost a decade when he surrendered in the information-loss bet and when he did, he also published a paper where he "rediscovered a solution" to all these issues. So although Hawking is clearly ignoring lots of important work – and I would probably mention or add other very important papers (Raju+Papadodimas, Maldacena+Susskind) that Hawking is ignoring – it seems a bit weird to describe Hawking as a person who should act as a "modest newcomer" to the discipline of the black hole information loss debates. He is still the very founder of this discipline, Clifford! ;-)

I doubt that Hawking can read all the papers. It's my guess that he must be skipping even some of the important ones. So I could enumerate you a few papers by Andy Strominger and a few dozens of others that Hawking has probably read, and then – except for all the TRF blog posts – he may be unaware of what's going on. Given the special circumstances, unlike Clifford, I would personally tone down my criticism of Hawking for his "not paying attention to everything that others are doing". He's still an incredible mind who has produced amazing things and who still has a noticeable probability of producing something very valuable and I think it's counterproductive to try to impose some "equations quota" (sponsor: Matt) or "number of references quota" (sponsor: Clifford) on this extraordinary physicist. Sorry, Matt and Clifford, but in my opinion, people should try to make the publication process for Hawking as simple as possible because every small simplification can make a difference.

**Sabine Hossenfelder**

Sabine Hossenfelder says that "there is nothing new here", ignore the media buzz, Hawking isn't saying anything new, and so on. From some viewpoint, it's right, but with the detailed connotations she means, it's crazy. She says that Hawking is just saying similar things to her and Lee Smolin who would write a paper proposing mathematically impossible modifications to the black hole geometry and refocusing on the apparent horizon – yes, Hossenfelder is surely among those who immediately jump on every bandwagon that carries nothing else than misconceptions.

Well, when two people are doing the same thing, it isn't the same thing. Sabine Hossenfelder hasn't written a single paper in her life whose basic content would be correct and new at the same moment. Her being treated as a physicist is due to some people's preference for papers written without the help of any Y chromosomes over papers with an intrinsic scientific value.

So if and when she says something new and radical i.e. stupid about black holes, nobody cares because she has done the same thing 100 times in the past and no one cared, either. But Hawking is the founder of the field and he has said and written many things that were both true and important – especially but not only in the early and mid 1970s – so if he says something radical, people are just paying attention.

I am not saying that famous people's work should ultimately be evaluated differently. But I am saying that when it comes to the initial reaction to people's papers (and whether we read them or not), the authors' previous record undoubtedly does matter. And I am saying that a chronic junk paper producer's new wrong statement is a smaller deal than an important physicist's new radical pronouncement – one that turns out to be wrong, too. Sabine Hossenfelder wrote:

In summary, nothing has changed in our understanding of black holes due to Hawking’s paper.For various reasons, this sentence may be true for all interpretations of the words but whether or not it is tautological depends on the interpretation of the word "our", among others. If she means people like herself, it's right that Hawking's new short paper hasn't changed anything about her understanding of the black holes – but the same is true for all important papers about quantum dynamics of black holes, too. They haven't changed her understanding of these topics; they have kept it at zero because she hasn't understood anything in this field.

**Summary: great quantum BH research exists but the people doing it are way below the critical mass**

At any rate, the degree of disharmony about these quantum black hole questions has become very high. I don't think that this reflects the intrinsic uncertainty concerning all such questions. Many lessons from classical general relativity, quantum mechanics, quantum field theory in curved spaces as an approximate description, and string theory including AdS/CFT are very clear and sharp and good researchers are trying to be aware of all the sufficiently well-established and important ones and develop a new specific, more (approximately) local picture of the black hole information that is compatible with the things we know from other sources.

Many others are unfamiliar with many important constraints. Too high a percentage of the radical claims about the quantum dynamics of the black holes only shows the "audacity" with which people are willing to throw some established results away completely. The real issue is that general relativity involving the black hole spacetimes is incompatible with quantum mechanics if you assume it "completely strictly"; but if you acknowledge that general relativity may have "small deviations in various quantities" – which is reasonable because the classical general relativity has no reason (no empirical reason and no theoretical reason) to "hold completely exactly" – then the compatibility reemerges.

And the minimal necessary modifications of GR needed it to preserve the information and reconcile it with quantum mechanics are tiny, indeed. I want to say that the people who are able to show that the deviations may be really tiny – the people who respect the well-established insights on both sides of the reconciliation – are the natural leaders of the field. Those who are willing to throw away some established principles or approximations completely are outliers or fringe groups. The basic rules of this "content" are clear: one tries to be as accurately compatible with things that should hold exactly or approximately, and the closer you get with a specific enough, internally consistent picture, the better you are.

With this self-evident conservative benchmark, Hawking was surely the leader of the field for quite some time since his 1974 revolution. I think that there are other leaders today and their work is almost never discussed by the media. It's not just the media, it is really the broader physics community – even theoretical physics community – that has become largely unaware of who is the real leader in this field. In this respect, the current situation is worse than the situation of many moments in the past. In the 1970s, people would surely know that 't Hooft or Hawking were the "big minds" to follow; the gospel would spread through some orderly enough channels. Today, the media and similar noise dominates; this awareness is arguably gone and that's too bad.

And that's the memo.

## snail feedback (9) :

Hey Lubos,

while I of course agree that an event horizon is an incredibly useful approximate concept, I do wonder how you imagine the Penrose diagram to look like for the entire history of a black hole. You correctly point out that black holes leave no remnants and that information is not lost. So I am sure you would agree that if one forms a black hole out of collapsing matter and lets it sit there for a very long time (or maybe not so long if we are talking about large extra dimensions and some small TeV black hole) eventually the black hole is gone, gone, gone and all I have left is flat space and outgoing Hawking radiation. While the complete evaporation does not happen in the semi-classical description, you surely agree that this is the right picture in the full quantum theory. I don't think you can draw a Penrose diagram for this full history that has a true event horizon in the sense that there are regions of the spacetime that are not in the causal past of future null infinity. Isn't this all that Hawking says?

Andreas

Dear Andreas, thanks for your visit. Well, first of all, the 2D Penrose diagrams are only good for "effectively 2D" situations, e.g. for 3+1D solutions with the full SO(3) rotational symmetry. So I can't draw a realistic 2D Penrose diagram for our 11D or 10D (and not even for their 4D) spacetime. ;-) The 2D picture doesn't even allow the black hole interiors to be too disconnected (several black holes) although this is clearly possible in the real higher-dimensional world, and so on.

Different portions of the 4D cosmology admit the causal diagram and various cosmology's causal diagrams have been drawn many times. I don't think I have something revolutionary to add here. I believe them. In some sense, I believe that the events behind a cosmic (de Sitter) horizon are unphysical for the particular observer in the middle but I still think that the classical spacetime may be useful for some "further away" observers and the patches of different observers overlap so they "effectively" allow us to reconstruct the whole classical spacetime including the regions behind the event horizons.

ER-EPR teaches us, I believe, that not only the precise "background geometry" but even its topology is largely a convention, so we may only pick the "classical geometries and topologies that are more useful" in the sense that the degrees of freedom on them are small perturbations of the pre-existing background, but there are no "universally right or wrong" backgrounds for a particular state.

I just completely disagree with you that an evaporating black hole doesn't have an event horizon. If has an event horizon because it has the interior - the points from which all light and massive particles inevitably hit the singularity, not scri plus. Do you disagree that with this definition of the black hole interior and the horizon, the Penrose diagram posted in this blog post does have an event horizon? Or do you think that this Penrose diagram is "wrong even as an approximation" for the classical geometry we see in the real-world evaporating black hole? If you do, I would like you to say more about your disagreement.

So we probably agree what Hawking is saying but I just think that both of you are totally wrong!

"

Sabine Hossenfelder hasn't written a" Sabinesingle paper in her life whose basic content would be correct

is a theorist, as are you. Elegant,

rigorous, eldritch derivation (

Phys. Rev. Dapproaching א_0) sums tonothing if a postulate is empirically falsified. You don't know the empirical answer either.

Alltheory is sour if the Equivalence Principle can bemeasurably, reproducibly violated (BRST invariance and string theory). Physics

cannot violate the EP. arxiv:1401.4784 will be net zero to 16 sig figs.

Chemistry delivers EP violation up to 10^(-12) difference//average in

five different ways, contradicting no prior observation. The gobsmacking

answer need not sit under the streetlight. History says it usually

doesn't. Look the

other way.Thanks for this article. I feel it dispels much of the confusion surrounding these issues.

I did not (yet) read the post in its entirety (shame on me), but regarding your question

> The diagram is very different if you turn it upside down. Is that a problem?

I do think it's a problem in a similar way that I consider Norton's dome to be a problem:

Falling into the singularity is fine (same as rolling upwards and coming to a stop at the top of the dome). However, if you reverse the process, you have particles being spontaneously emitted from the singularity (or things starting to unpredictably roll downwards, respectively).

However, there's a resolution to this issue and I'd like to hear your thoughts on it:

Apparently, black hole singularities aren't topological or even differential in nature. Choosing the right set of coordinates, it can be shown that they are 'just' degeneracies of a well-defined, smooth metric.

Mathematically, such degeneracies will break the framework of Riemannian geometry, but that's just our toolset being insufficient.

Physically, one can think of the degeneracy as a case of dimensional reduction - but because spacetime remains smooth, worldlines can be extended right through the singularity.

See Cristi Stoica's [arXiv:1207.5303](http://arxiv.org/abs/1207.5303) for the short version and [arXiv:1301.2231](http://arxiv.org/abs/1301.2231) for the long one.

Hi Lubos: Excellent summary for non experts like me. I am in the process of gradually understanding the controversy! I am puzzled though. BH of astronomical size would take billions and billions of years to evaporate by Hawking radiation via quantum tunneling. That is why people have seen matter

falling in but not coming out. If the emission is fast we would have surely seen it. So my question is how does Hawking slow down the emission of Hawking radiation without event horizon? Is his disappearance of (apparent) event horizon a function of time?

Isn't this apparent horizon vs event horizon business really just a matter of nomenclature convention. When we talk about an event horizon in a fixed background (the eternal Schwarschild black hole) as in the above Penrose diagram we are clearly working in the approximation where backreaction from quantum corrections are ignored. In this approximation, it really is an event horizon and not an apparent horizon.

However in the more general quantum and formal statement where backreaction is not ignored, and where the metric degrees of freedom are probably not quite right we are allowed to say that the horizon was only transient in nature. (we probably should call it an apparent horizon with a hat)

Agree 100% , and I doubted that intelligent people comment on this blog.

It should have been Ltom, you imbecile. Learn how to memorize the order of 2-4 letters before you spam the Internet by the worthless support of demonstrably wrong opinions by your worthless would-be brain.

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