I have a multiple choice question for you.

What’s inside a black hole?

(A) An unlimited amount of stuff.

(B) Nothing at all.

(C) A huge but finite amount of stuff, which is also outside the black hole.

(D) None of the above.

The first three answers all seem absurd, boosting the credibility of (D). Yet … at the “Rapid Response Workshop” on black holes I attended last week at the KITP in Santa Barbara (and which continues this week), most participants were advocating some version of (A), (B), or (C), with varying degrees of conviction.

When physicists get together to talk about black holes, someone is bound to draw a cartoon like this one:

I’m sure I’ve drawn and contemplated some version of this diagram hundreds of times over the past 25 years in the privacy of my office, and many times in public discussions (including at least five times during the talk I gave at the KITP). This picture vividly captures the defining property of a black hole, found by solving Einstein’s classical field equations for gravitation: once you go inside there is no way out. Instead you are unavoidably drawn to the dreaded singularity, where known laws of physics break down (and the picture can no longer be trusted). If taken seriously, the picture says that whatever falls into a black hole is gone forever, at least from the perspective of observers who stay outside.

But for nearly 40 years now, we have known that black holes can shed their mass by emitting radiation, and presumably this process continues until the black hole disappears completely. If we choose to, we can maintain the black hole for as long as we please by feeding it new stuff at the same rate that radiation carries energy away. What I mean by option (A) is that the radiation is completely featureless, carrying no information about what kind of stuff fell in. That means we can hide as much information as we please inside a black hole of a given mass.

On the other hand, the beautiful theory of black hole thermodynamics indicates that the entropy of a black hole is determined by its mass. For all other systems we know of besides black holes, the entropy of the system quantifies how much information we can hide in the system. If (A) is the right answer, then black holes would be fundamentally different in this respect, able to hide an unlimited amount of information even though their entropy is finite. Maybe that’s possible, but it would be rather disgusting, a reason to dislike answer (A).

There is another way to argue that (A) is not the right answer, based on what we call AdS/CFT duality. AdS just describes a consistent way to put a black hole in a “bottle,” so we can regard the black hole together with the radiation outside it as a closed system. Now, in gravitation it is crucial to focus on properties of spacetime that do not depend on the observer’s viewpoint; otherwise we can easily get very confused. The best way to be sure we have a solid way of describing things is to pay attention to what happens at the boundary of the spacetime, the walls of the bottle — that’s what CFT refers to. AdS/CFT provides us with tools for describing what happens when a black hole forms and evaporates, phrased entirely in terms of what happens on the walls of the bottle. If we can describe the physics perfectly by sticking to the walls of the bottle, always staying far away from the black hole, there doesn’t seem to be anyplace to hide an unlimited amount of stuff.

At the KITP, both Bill Unruh and Bob Wald argued forcefully for (A). They acknowledge the challenge of understanding the meaning of black hole entropy and of explaining why the AdS/CFT argument is wrong. But neither is willing to disavow the powerful message conveyed by that telling diagram of the black hole spacetime. As Bill said: “There is all that stuff that fell in and it crashed into the singularity and that’s it. Bye-bye.”

Adherents of (B) and (C) like to think about black hole physics from the perspective of an observer who stays outside the black hole. From that viewpoint, they say, the black hole behaves like any other system with a temperature and a finite entropy. Stuff falling in sticks to the black hole’s outer edge and gets rapidly mixed in with other stuff the black hole absorbed previously. For a black hole of a given mass, though, there is a limit to how much stuff it can hold. Eventually, what fell in comes out again, but in a form so highly scrambled as to be nearly unrecognizable.

Where the (B) and (C) camps differ concerns what happens to a brave observer who falls into a black hole. According to (C), an observer falling in crosses from the outside to the inside of a black hole peacefully, which poses a puzzle I discussed here. The puzzle arises because an uneventful crossing implies strong quantum entanglement between the region A just inside the black hole and region B just outside. On the other hand, as information leaks out of a black hole, region B should be strongly entangled with the radiation system R emitted by the black hole long ago. Entanglement can’t be shared, so it does not make sense for B to be entangled with both A and R. What’s going on? Answer (C) resolves the puzzle by positing that A and R are not really different systems, but rather two ways to describe the same system, as I discussed here.That seems pretty crazy, because R could be far, far away from the black hole.

Answer (B) resolves the puzzle differently, by positing that region A does not actually exist, because the black hole has no interior. An observer who attempts to fall in gets a very rude surprise, striking a seething “firewall” at the last moment before passing to the inside. That seems pretty crazy, because no firewall is predicted by Einstein’s trusty equations, which are normally very successful at describing spacetime geometry.

At the workshop, Don Marolf and Raphael Bousso gave some new arguments supporting (B). Both acknowledge that we still lack a concrete picture of how firewalls are created as black holes form, but Bousso insisted that “It is time to constrain and construct the dynamics of firewalls.” Joe Polchinski emphasized that, while AdS/CFT provides a very satisfactory description of physics outside a black hole, it has not yet been able to tell us enough about the black hole interior to settle whether there are firewalls or not, at least for generic black holes formed from collapsing matter.

Lenny Susskind, Juan Maldacena, Ted Jacobson, and I all offered different perspectives on how (C) could turn out to be the right answer. We all told different stories, but perhaps each of us had at least part of the right answer. I’m not at KITP this week, but there have been further talks supporting (C) by Raju, Nomura, and the Verlindes.

I had a fun week at the KITP. If you watch the videos of the talks, you might get an occasional glimpse of me typing furiously on my laptop. It looks like I’m doing my email, but actually that’s how I take notes, which helps me to pay attention. Every once in a while I was inspired to tweet.

I have felt for a while that ideas from quantum information can help us to grasp the mysteries of quantum gravity, so I appreciated that quantum information concepts came up in many of the talks. Susskind invoked quantum error-correcting codes in discussing how sensitively the state of the Hawking radiation depends on the information it encodes, and Maldacena used tensor networks to explain how to build spacetime geometry from quantum entanglement. Scott Aaronson proposed the appropriate acronym HARD for HAwking Radiation Decoding, and argued (following Harlow and Hayden) that this task is as hard as inverting an injective one-way function, something we don’t expect quantum computers to be able to do.

In the organizational session that launched the meeting, Polchinski remarked regarding firewalls that “Nobody has the slightest idea what is going on,” and Gary Horowitz commented that “I’m still getting over the shock over how little we’ve learned in the past 30 years.” I guess that’s fair. Understanding what’s inside black holes has turned out to be remarkably subtle, making the problem more and more tantalizing. Maybe the current state of confusion regarding black hole information means that we’re on the verge of important discoveries about quantum gravity, or maybe not. In any case, invigorating discussions like what I heard last week are bound to facilitate progress.

Kostiantun RopotenkoAugust 29, 2013 at 6:49 amI think that C is a correct answer. In brief, my idea is as follows. In Euclidean approach the temperature of a black hole is defined as T=k/O, where k is the surface

gravity of a black hole and O is an angular variable, O=2pi. But O can be negative. Since T>0, it follows that k>0 when T=+2pi, and k<0 when O=-2pi. The state with k0 and other with k<0. Then the entropy goes like the area and information can be recovered from the black hole, as required.

Kostiantyn RopotenkoAugust 29, 2013 at 12:04 pmUnfortunately, the last part of my comment was scrambled and lost during submitting. Sorry. Here is a corrected version. “The state with k0 and other with k<0. Then the entropy goes like the area and information can be recovered from the black hole, as required”.

Vasil PenchevAugust 29, 2013 at 7:04 am(D) = (A)&(C)=An unlimited amount of stuff, which seems finite outside and thus as a black hole = a universe like ours inside.

Jon AwbreyAugust 29, 2013 at 7:36 amJust a know-nada question —

If gravitation is mediated by gravitons, then it seems they must be leaving the neighborhood of the singularity all the time … what’s up with that?

preskillAugust 30, 2013 at 9:15 amWhat happens at the singularity is the most important part of the question about what is inside a black hole. We don’t know the answer. If (B) is correct, then the singularity is right at the horizon, and the picture I drew is incorrect.

K.C. Lee, M.D., North Bethesda, Maryland.August 31, 2013 at 5:22 pmIf the following is consistent with what happens at the singularity, multiple choice (D) may be an answer because:

1. At entanglement, spacetime is created (Swingle and van Raamsdonk).

2. This classical spacetime comes from, for lack of suitable terminology, quantum spacetime*.

3. At a singularity, the reverse of items 1 and 2 takes place.

In support of item 2 may be the double slit experiment. Where a photon, existing in probability quantum spacetime, seemingly spanning both (and any number of additional) slits, at measurement/entanglement, acquires determinate properties in the classical spacetime created per item 1.

*This quantum spacetime may be thought of as some probability (virtual) space at an instant in time. This probability-based scheme is different from the quantum spacetime schemes that have been proposed, in that it is non-physical, and bears no link at all to classical spacetime.

If item 3 is true, at the black hole singularity, classical spacetime is replaced by quantum spacetime where matter resumes a probability “existence”. They will stay in that “virtual” state until the next measurement or entanglement. As such, unlike in classical spacetime, quantum spacetime does not involve a physical singularity, where general relativity laws cease to apply.

This proposed spacetime “recycling” scheme in items 1 and 3 could be a simple way to tackle many paradoxes. Most of which arise because the inappropriate spacetime is applied. Be it thinking in terms of classical spacetime at quantum situations, or vice versa.

Staying with the black hole as an illustration, quantum spacetime rather than classical spacetime should be in play. As such, Hawking radiation, as a quantum event, has no problem. The event horizon, on the other hand, could be the unnecessary product of an unwillingness to sever the umbilical cord with Einstein. With quantum spacetime at the black hole, being non-physical, not only the event horizon, but the need for a firewall, holography, AdS/CFT, No Drama and likely even the information paradox, etc. all vanish.

This recycling of spacetime provides for the coexistence of general relativity and quantum mechanics. The key is to ensure appropriate switching between classical and quantum spacetime as the need arises.

K.C. Lee, M.D., North Bethesda, Maryland.September 1, 2013 at 11:52 am1) A key element of the proposed spacetime recycling scheme was inadvertently omitted: the role played by gravity.

The creation of classical spacetime at entanglement (James Swingle and Mark Van Raamsdonk) occurs at low gravity situations, as we commonly experience. In contrast, quantum spacetime appears at high gravity environments, such as the black hole.

What could influence which gravity situation prevails? One candidate is the combined opposing strengths of dark matter and dark energy. Where (and when) dark matter trumps dark energy in the universe, one should encounter high gravity. This obviously needs proof as well.

2) The issue of the information paradox was left somewhat open. Strictly speaking though, the paradox was framed in classical spacetime terms mainly. As such, it may not have the same implication and import in quantum spacetime. For instance, we do not usually note that Hawking radiation adds new information. By the same token, we may not need to focus so doggedly on the “loss” of information at a black hole.

3) On reversibility. Classical spacetime creation at entanglement should not be reversible, just as wavefunction collapse is irreversible. At the black hole, quantum spacetime appearance is likewise not reversible. Viewed in totality, the whole cycle of spacetime switching from classical to quantum also takes place in one direction, depending on gravity, whereby:

At low gravity:

“Nothing is anything until entanglement makes everything something.”

(A case of relation without relata in relational ontology philosophy.)

At high gravity:

“Everything turns back into nothing.”

With spacetime recycling:

“Nothing ends up being something, again.”

Certainly consistent with a cyclic universe model.

K.C. Lee, M.D., North Bethesda, Maryland.September 2, 2013 at 5:37 pmCorrection: Brian Swingle. (Not James).

Stam NicolisSeptember 1, 2013 at 2:41 amIsn’t it true that for an extremal black hole (e.g. Reissner-Nordstrom, with M=|Q|), the singularity is, indeed, at the horizon(s) (since the outer and inner horizons then coincide)?

Stam NicolisSeptember 1, 2013 at 3:35 amSo would it be true to say that, for an extremal black hole, (C) is true, since an extremal black hole doesn’t have an interior-so, in that sense, (B) doesn’t apply and infalling `probe’ matter (that doesn’t affect the extremality condition) “spreads” on the horizon?

James T. DwyerSeptember 1, 2013 at 4:08 amIf infalling matter is disintegrated at the horizon, with its released mass-energy retained within the event-horizon and its residual material particles ejected, there is no retention of dimensional matter anywhere. As I understand, high energy particle interactions emitting X-rays within the inner portion of accretion disks, and relativistic polar jets are observed features of many active black holes, and though to also occur during stellar core collapses – seemingly consistent with this conception. Please see my other comments (below)…

John BaezAugust 30, 2013 at 7:22 pmIf gravity is mediated by gravitons, the math suggests it’s a lot like how electromagnetism is mediated by photons. When you have a charged particle it’s surrounded by an electric field, much as a massive object is surrounded by a gravitational field. But this electric field doesn’t consist of actual photons leaving the charged particle, like light leaves a flashlight – it consists of virtual photons. Virtual particles are tricky; they can “go faster than light”… so there’s no difficulty for the gravitational field to “get out” of the black hole. (The phrase “get out” is a bit confusing in the first place, because it’s not as if the gravitational field were originally stuck inside the black hole: it was always already out.)

Jon AwbreyAugust 30, 2013 at 7:28 pmThanks for the explanation❢

Shtetl-Optimized » Blog Archive » FirewallsAugust 29, 2013 at 9:35 am[…] (Aug. 29): John Preskill now has a very nice post summarizing the different views on offer at the firewall workshop, thereby alleviating my guilt for […]

moriturimax (@moriturimax)August 29, 2013 at 10:40 amIf the mass of a black hole decreases, does entropy also decrease?

moriturimax (@moriturimax)August 29, 2013 at 10:44 amI wonder if information encoded in a black hole is used as the seed for the next iteration of the universe, thus making sure all the constants are setup the same way again?

preskillAugust 30, 2013 at 9:17 amYes. The entropy is proportional to the area of the black hole’s horizon, which is proportional to the square of its mass. The entropy decreases as the black hole radiates away energy, reaching zero as the black hole disappears.

James T. DwyerSeptember 1, 2013 at 3:47 amAs I understand, only tiny (primordial) black holes are thought be diminished by Hawking radiation, as black holes with larger horizons are thought to absorb sufficient CMB radiation to offset the tiny Hawking radiation. Even tiny black holes can also accrete matter – offsetting much Hawking radiation, correct?

More to the point, isn’t Hawking radiation thought to diminish BH by virtue of its negative energy – attributed to the ingested particle of a virtual pair made persistent solely to offset the accounting of mass-energy conservation for the emitted particle, which seems to have come from nowhere?

Actually, though, shouldn’t the energy of transient virtual particles already be accounted for by their diminishment of vacuum energy? In this case, wouldn’t there be no requirement to offset the persistence of emitted Hawking radiation by negating the energy of the ingested particle? Shouldn’t then the ingested energy be positive, incrementing rather than decrementing black hole mass-energy?

lpsingh02August 29, 2013 at 11:15 ami think it is a hole in the plain of time and space. Nothing exists in them. They are just bullet holes caused by matter too dense for our time/space to support. Atoms itself are broken down to the most primitive forms (pre-big bang state)….or not. 😀

PlatoAugust 29, 2013 at 11:54 amJust seeing scientists categorized in this way is most interesting. So all views points about black holes for the lay public can be generalized in this way?

Peter ShorAugust 29, 2013 at 2:07 pmNobody at the workshop seems to have come up with my favorite answer: both A and B (but not C). I suppose I should write something up.

preskillAugust 30, 2013 at 9:17 amPlease do!

K.C. Lee, M.D.August 31, 2013 at 6:36 amYou stated, “Answer (C) resolves the puzzle by positing that A and R are not really different systems, but rather two ways to describe the same system …”.

If by that you meant to employ a EPR=ER wormhole as a solution, does it not negate the existence of the black hole itself, by equating space-time inside and outside of the black hole?

yangAugust 29, 2013 at 3:45 pmIf everything cant escape from the black hole, then how can gravitons escape and effect the matters outside the horizon? So my guess is C or D

Two Cultures | Not Even WrongAugust 29, 2013 at 8:29 pm[…] Update: A summary of the situation from John Preskill is here. […]

ColumbiaAugust 30, 2013 at 1:52 amOne of the things that would be nice, would be to sharpen our arguments against A. Losing boundary unitarity naively seems very drastic and contrary to Ads/cft and quantum mechanics in general. Unfortunately many of the old arguments like the loss of conservation laws and thermodynamic instability can be evaded or wiggled out off as Bob and Bill pointed out.

I feel like those old arguments should be revisited to rule out this scenario once and for all… I suspect that it should be possible in principle.

Peter ShorAugust 30, 2013 at 5:08 amColumbia: I think the results on Hamiltonians having natural error correcting abilities (i.e., Kitaev’s topological error correction codes and honeycomb lattice) show that there is nothing wrong with having unitarity at large scales and loss of information at small scales. In other words, it doesn’t really conflict with quantum mechanics. So you’re going to have to base your argument on AdS/CFT, which doesn’t actually apply directly to the universe we live in.

What I would really like is an explanation of how the information gets out of a black hole in the AdS/CFT universe. I think the fact that we don’t have one yet shows that AdS/CFT is really not very well understood.

pforndiazAugust 30, 2013 at 8:58 amPerhaps not very relevant scientifically, but for the science-fiction gang (who on the other hand have helped giving black holes the fame and respect they share among all kinds of non-scientific enthusiasts, something very few branches in physics can boast about), which of the options is most favorable? I am thinking in terms of what Prof. Hawking once said at conference in Caltech about the impossibility of the existence of portals to travel through space-time…

preskillAugust 30, 2013 at 9:11 amI think all the options provide potential fodder for science fiction. But (A) probably fits best with the notion that we can travel through a black hole to a new universe. (C) fits with the idea that a black hole is the mouth of a wormhole, but not the kind of wormhole we can travel through safely.

Alexander VlasovAugust 30, 2013 at 12:50 pmA technical question: If formation of EP bridges or something similar should be considered as (D) or it should not be included into classification as hot being true blackhole?

Alexander VlasovAugust 31, 2013 at 7:38 amSorry for mistypes, should be “ER bridges”, “not being true blackhole?”

E.L. WistyAugust 31, 2013 at 10:03 amReblogged this on Pink Iguana.

James T. DwyerAugust 31, 2013 at 10:05 amFor b) to be correct, infalling matter might be disintegrated into fundamental particles, releasing its nucleic binding mass-energy, which is retained as gravitational energy or contracted (curved) spacetime. The residual low mass charged particles could be ejected by magnetic fields, leaving the singularity as an empty, dimensionless focal point of gravitational energy.

Rich OlcottAugust 31, 2013 at 1:43 pmAn empty point, or a “hollow” sphere? The latter would be the Universe’s way of avoiding having a singularity at all. I’m visualizing the equivalent of a hurricane — from a distance it looks like a singular “point” attracting incoming matter, but close-up, all the turbulence and disruption is at the vortex boundary rather than at the geometric center.

James T. DwyerAugust 31, 2013 at 4:29 pmWhy not a dimensionless point, as long as it is not required to contain matter? It can exist in reality as a geometric focal point for directionally contracted/curved spacetime. As long as collapsing atoms disintegrated, allowing dimensional particles to be ejected prior to entering the event horizon, there is only the unbound mass-energy retained as contracted spacetime.

There is no form of matter that could support an object of any dimensions containing the mass-energy of millions of solar masses, for example. In this way there should be no objection to a singular focal point of geometrically curved contracted spacetime.

Rich OlcottAugust 31, 2013 at 4:58 pmParsimony, basically. A singularity in the apparent solution to a physical problem is generally taken to be an indication that the mathematical model doesn’t properly cover the situation — integrals across the singularity go to infinity, sometimes even abruptly changing sign from one side to the other, that sort of thing. If we can revise the model to avoid a singularity, experience has shown that the revision is a better representation of the system and can lead to more reliable tests of the theory behind the math.

James T. DwyerAugust 31, 2013 at 5:22 pmIMO, no such objections should apply to what is effectively the center of mass…

Jay TrudeauAugust 31, 2013 at 8:59 pmInteresting idea about the “hollow sphere”. Have a look at the book “Hidden In Plain Sight 2” by Andrew Thomas for a similar idea.

James T. DwyerSeptember 1, 2013 at 2:23 amPerhaps to clarify, if the answer to: “What’s inside a black hole?” is

“(B) Nothing at all”, then I suggest that its structure is that of an empty sphere or ellipsoid whose energetic surface, near the event horizon, disintegrates all infalling matter, retaining released nucleic mass-energy that had previously been derived from the confinement of quark kinetic energy within nuclei by binding gluons. No residual dimensional matter enters the event horizon – it is expelled by peripheral EM interactions via relativistic polar jets. Within the interior of the the “hollow sphere”, there is nothing but gravitationally contracted, curved spacetime, directed towards a singular focal point.

To my limited knowledge, the empty sphere of answer (B) originated with Kip Thorne, although he considered that material fell through to a singularity, where it was crushed, converted into gravitational energy. I suggest that the high energy nuclear processing of matter occurs near the event horizon, never entering the superluminal conditions within the event horizon, as evidenced by X-ray emissions observed very close to the interior of hot accretion disks.

I suggest that the residue of dimensional material disintegration – resulting from the extraction of atomic mass-energy near the event horizon – is expelled through the observed high energy relativistic polar jets exhibited by forming and active black holes that are converting material mass-energy into gravitational energy.

It’s intended that this simple conceptual overview can be considered to be generally consistent with both general relativity and quantum mechanics, producing the predicted fundamental characteristics of black holes that are consistent with and to some extent explaining their observed characteristics.

James T. DwyerSeptember 1, 2013 at 3:33 amActually, I find where Kip Thorne attributes the idea of a black hole ass empty spacetime to John Wheeler. Please see dx.doi.org/10.1126/science.1225474

“In the 1950s and ’60s, John Archibald Wheeler speculated that curved, empty spacetime could exhibit rich, nonlinear dynamics—which he called geometrodynamics—analogous to the writhing surface of the ocean in a storm. Wheeler urged his students and colleagues to seek insight into geometrodynamics by solving Einstein’s general relativity equations (1).

“Motivated by Wheeler and by the 1963 discovery of quasi-stellar radio sources (quasars), physicists identified black holes as “gravitational solitons”—objects made wholly and solely from curved spacetime, objects whose curvature is generated by the energy stored in the curvature. From general relativity, they deduced that black holes can spin and oscillate; that the evolution of a black hole is governed by a set of physical laws that resemble the laws of thermodynamics; and most famously that, if a black hole is tiny, it can emit Hawking radiation due to quantum effects and thereby gradually evaporate (2).”

Lucractius (@lucractius)September 1, 2013 at 10:31 amThanks for the ‘gravitational soliton’ mention, I now look forward to having something to research around that may explain some of the theoretical work underpinning the answer to the question i posed down here http://quantumfrontiers.com/2013/08/29/whats-inside-a-black-hole/comment-page-1/#comment-4487

James T. DwyerSeptember 1, 2013 at 12:34 pmYou’re welcome – glad to be of even some small, incidental assistance!

CFTAugust 31, 2013 at 1:40 pmBlack hole logic 101

1.First assume there is such thing as a singularity in actuality, which is a point in space with zero size, not small mind you, zero size. So in essence it is a mere location.

2.Now assume you can assign mass or density to said point. You will have to jettison primary school geometry and arithmetic since you will need to multiply L*W*H (which are all zero) and somehow get a positive volume with which you can calculate density…hmmm…. well, hand wave a bit and pretend “the metric blows up”, next you must call this creation a ‘singularity’ since saying ‘you mean there’s nothing there?!!’ or ’empty space’ makes it harder to convince others your empty location can be made into a mathematical fiction which can be made into a physical actuality which can magically have the properties of size and density while having neither.

3.Next, assume you can have a mathematical space in general relativity with Ric=0. This means all matter has been removed from your eternal, asymptotically flat space (it has no curvature whatsoever) …and shove your infinitely dense singularity into this space which is described in HIGHLY NON LINEAR field equations…then assume/pretend the NON LINEAR nature of Einstein’s GR equations does not mean you can’t shove matter into it… Just like Hawking and Penrose did. note: you will also have to jettison algebra too now it appears…its all for a good cause of course.

4.Assume there actually is a solution for Einstein’s field equations for two or more bodies… despite the fact there isn’t one…but don’t let that stop you.. just wave your hands some more and use lots of mathematical sounding buzz words!

5.Assume Einstein (or his fans) knows what ‘r’ is. It can’t be a radius. Having any kind of radius calculated from of a zero sized mathematical abstraction does seem to keep pushing that multiplication/division by zero problem thingy, but hey, no worries. Don’t worry about the pesky little fact that there are almost a dozen different definitions for ‘r’…most likely all of them wrong.

6.Assume you can divide by zero… sigh…and get infinity to make the math work…and watch out when the metric “explodes”…this ‘explodes’ or ‘blows up’ part must be why they don’t let you divide by zero in highschool ….it’s much too dangerous you see…flying bits and pieces of math going every which way, putting out eyeballs and all that. Hawking thinks this exploding metric is awesome, as it allows other large but finite numbers with the “$” symbol in front of them to represent his book sales.

7.Assume all the wondrous assumptions you’ve stacked up are A-OK, and you can proceed to failed logic 101 where you talk about what “outside a body” means in a space that contains no body or matter whatsoever, only an abstraction called a point (a point does not exist physically, only as a locational abstraction) which has no dimension (meaning zero body to be outside of), this is called ‘circular logic’ and can be made to go away with more hand waving and fancy terminology.

8. I think at this point you are ready to start talking authoritatively about ‘event horizons’, Hawking’s radiation, time travel, wormholes, pocket universes, multiverses, and falling into black holes in general etc. (ignore the two or more body technical difficulty with your model) where the abstract mathematical point you are calling a ‘singularity’ ‘is no longer a limiting mathematical fiction’ and becomes an actual ummm….thingy which somehow manages to become highly important to physics since it models….errr….infinite, flat empty space with no matter with which could possibly produce gravity…which is just like our universe….and will help us to understand…. err… ummm…Well, I’m sure it employs a lot of outstanding, super-mega-ultra-massively intellectual very super-smart people who really need to know what happens in our universe when they make up a hole that has literally no content but still manages to suck up vast amounts of time, space, and funding.

Joe MarchioneAugust 31, 2013 at 6:40 pmI am non-physicist observer … so my reply is more query than statement. D is my highly uneducated best guess. Why? Imagine that its possible in the extreme gravitational environment beyond the event horizon [presumably during some stage of spaghettification] that color charges are ripped from their respective Quarks and/or Gluons as they descend into quantum hell. If the accumulation of color charge is [at least theoretically] tied to the acquisition of mass, breaking this symmetry might mitigate a significant percentage of the presumed mass and gravity associated with the black hole and perhaps even eliminate the idea of a lurking singularity at its core. The surface beyond the event horizon might contain a staggeringly large aggregation of material information but in a surprising turn of events it produces far less gravitational effects below some critical surface boundary level than expected. The entropy of the black hole is therefore considerably lower than prediction and the small percentage of entropic radiated energy that is produced becomes entangled with the bare Quarks below it. The energy of entropy radiates inwardly rather than outwardly. So, Bob and Alice don’t exist and Ted is happily entangled with Carol [the bare naked lady no one knew about]. Two timing is avoided and no one is breaking any laws. There is no loss of information because it is all confined, some portion at the event horizon and the rest asymptotically coupled to bare massless particles below. I know this is a crazy idea but I have no reputation to risk by proposing it. I hope it is at least amusing. : )

Helyn MarxSeptember 1, 2013 at 10:20 amDoes a black hole even have an inside?

preskillSeptember 1, 2013 at 10:54 amThat’s part of the question. Answer (B) says no.

James T. DwyerSeptember 1, 2013 at 12:24 pmAs I envision it, option (B) indicates an interior dimensional spacetime, but one that is devoid of matter – its exterior surface of energetic quantum material interactions and transformations forms an empty ellipsoid…

K.C. Lee, M.D., North Bethesda, Maryland.September 1, 2013 at 12:29 pmIn the proposed spacetime recycling scheme, there is no event horizon (and all the paradoxes it generated). Classical spacetime ends right at the edge of the black hole.

The “inside” is governed by quantum spacetime rules, where everything is recycled into “nothing”. Ready for entanglement to turn these “nothing” into something where gravity is low again.

One way to rephrase is to say inside means where gravity is high and outside is where gravity is low.

Lucractius (@lucractius)September 1, 2013 at 10:26 amAs someone that likes physics and has a passing (if rusty, rough and inexpert) understanding of the sort of things one learns early on in the paths to degrees in such fields as cosmology, particle physics, quantum physics, etc. One thing always bugged me about discussions about the inside of a black hole’s event horizon.

Given the nature of the black hole event horizon as a discontinuity in the Time domain rather than the space domain as its more typically pondered. How can half the discussions I read about black hole physics make any sense at all?

The more time I think about it the more I wind up thinking about a black hole event horizon as a form of space time topological defect, quite likely a kind of ‘stable’ domain wall. The prediction that the interaction of 2 domain walls is likely to produce gravitational waves fits neatly with predictions orbiting black holes should produce gravitational waves. Is it possible to prove that a black hole event horizon isn’t a stable topological defect induced by the mind shatteringly huge energies involved in its creation, and that the answer to your question is simply (D) by virtue of the event horizon being for all intents and purposes, the edge of our ‘universe’, nullifying our effort to understand the physics beyond. And that any predictably applied physics we have been able to ‘map’ onto the event horizons studied so far, such as gravity, hawking radiation, etc, are all manifestations of the properties of the specific class of topological defect itself than indications of physics taking place on the other side of the defect boundary we know of as an ‘event horizon’.

I only ask out of curiosity, I’m not in the least attached to my hypothesis, merely an interested lay physicist wishing for answers they lack the money to spend the time learning. (Curse my choice of computer science over pure physics at university)

James T. DwyerSeptember 1, 2013 at 12:28 pmAs I understand, the event horizon presents a spacetime discontinuity only for distant observers – as the initially insignificant discrepancy increases with distance.

Lucractius (@lucractius)September 1, 2013 at 3:13 pmDoes that necessarily exclude it from still being a topological defect? I remember hearing of a number of wave like topological defects in various fields, soliton waves and such. And which makes me think that the defect can have a ‘gradual shape’ of some kind. Perhaps the central point of the black hole is merely the peak of the ‘wave’ that has an amplitude determined by the mass that formed it and has since been accrued, and the outer edges match what we see of its behaviour in space time regarding how it distorts it. I’ll certainly be taking a read of that material you mentioned up here. http://quantumfrontiers.com/2013/08/29/whats-inside-a-black-hole/comment-page-1/#comment-4480

Hopefully I’ll find at least something to quell my curiosity. It’s the most frustrating thing in the world having a question the answer doesn’t feel right to. Suppose thats where the old adage comes from “The greatest things in science aren’t found with ‘Eureka!’, but with ‘Hrmm, that looks funny…'” I’m sure its probably just something I don’t know about space-time that excludes this crazy sounding idea I’ve had lodged in my head.

James T. DwyerSeptember 1, 2013 at 5:10 pmI really can’t address from any theoretical context, but I think it can be considered a topological feature, for stellar core collapse BHs, certainly the product of the collapse of dimensional spacetime corresponding to the point directed acceleration of mass-energy.

My comment was intended to address your statement:

“Given the nature of the black hole event horizon as a discontinuity in the Time domain rather than the space domain as its more typically pondered.”

I think that the local contraction of space and dilation of time always correspond, but I’m no expert on the subject. Best wishes!

Lucractius (@lucractius)September 1, 2013 at 9:22 pmA-ha! sorry about that paragraph 🙂 After writing it and submitting it I immediately realised how clumsy that bit sounded. What I was trying to convey was a bit of the background why I wound up pondering the event horizon as a topological feature instead of a gravitationally induced space-time effect in the first place.

The interplay between space and time in the region of the horizon, and how most discussions [ That I can follow at least 🙂 ] seem to only be discussing the region as if it were normal space, devoid of any time effects. Lead me to ponder the implications of the black hole as a simulacrum of the great cosmological horizon which is due more to the time in question than the distance. Which wound up with a great deal of pondering over the little I can claim to know of the holographic principle, the quantum vacuum field, the cosmic microwave background and the curious notion that popped out the other end of all the thinking was that perhaps the CMB we see when we look at the cosmic particle horizon, is the ‘inside’ version of the hawking radiation we see on the outside surface of a black hole. From there it was a short hop to ‘pocket universes’ and the question of domain walls and the rest of my topological pondering.

But being nearly 2am when I typed it. I seem to have failed to explain almost all of what I intended to say before asking my question. Looking at it now, I’m just glad I got my question typed out how I wanted haha.

Ajit R. JadhavSeptember 1, 2013 at 11:14 pmYawn. … Such a (mostly) boring stuff! …

… It’s obviously something like (C), though many qualifications and modifications would apply (though it seems that such things are not very obvious to every one): (i) a literal singularity cannot physically exist (and is merely an oddity of the nature of the mathematical model used in describing the pertinent physical reality—something similar to the singularity in stress at material interfaces, or better still, at the crack-tip, in solid/fracture mechanics); (ii) for light not to ordinarily escape, no _literal singularity_ is anyway necessary; (iii) (as a plain consequence), stuff outside and inside can of course be distinguished; (iv) [don’t understand too clearly what “firewall” is supposed to mean, but, what the heck, this is just a blog comment!] there cannot be an infinite firewall—just the way there cannot be an infinity of anything concretely physical; and if not infinite, what should it create an issue? (v) “information” cannot (and does not) get lost when stuff and/or light falls in (regardless of whether there is a firewall or not, and regardless of the manner in which the fallen stuff might eventually come out)…

No, but I am not one of those “one-half too smart” (original Hindi: “deDh shahaaNaa”) types—am not permanently so, anyway! 🙂 … As I said, I don’t understand exactly what firewall is supposed to mean, or plain, even, if there is any general agreement about its meaning at all or not. … And, I don’t think I understand really well what it means to say that entanglement cannot be shared—the simple-minded “analysis” suggests that, taking the the global view (i.e., taking a _local_ view of QM and then extending it to apply to the universe as a whole), entanglements are always “shared,” aren’t they? Or do I have something way too half-baked here?… Come to think of it, this last issue makes it a bit less boring… What comprehensive physical argument—if any—exists to deny “sharing” of entanglements…

[Won’t necessarily post replies to any sub-comments that this comment might generate—and I (really) hope that it does not! … Just noting down/passing along what _seems_ to be the case, that’s all…]

Ajit

[E&OE]

John SidlesSeptember 2, 2013 at 12:30 pmLet us define “quantum systems engineering” to be the restriction of quantum physics to the question: “What are the most efficient (classical) Turing Machines (TMs) that predict the output of quantum simulations?”

It is clear that this TM-based definition separates firewall physics from quantum systems engineering, for the common-sense reason that we don’t know how to simulate quantum black hole dynamics on TMs (even in principle).

However, objects that we will call “quantum greyholes” — which naturally instantiate many of the dynamical attributes of quantum black holes—can be simulated (to arbitrary precision) on TMs, and thus are properly within the domain of quantum systems engineering, as follows.

We consider the Hilbert-space dynamics associated to a basis of (say) 2^12 interacting qudits. Depending on the assignment of couplings between qudits, the transport properties of the system can be effectively 1-d (a 1D toroid array of 4096 qudits), or 2-d (a 64×64 toroidal array of qudits), or 3-d (a 16x16x16 toroidal array of qudits), or even a disordered Borel set of qudits, in which the qudit couplings yield a quantum dynamics that has no description in terms of spatially localized transport.

Consider the blended case of a 64×64 qudit toroid, in which the couplings of an 8×8 subblock are randomized, such that the aggregate “universal” dynamics is characterized by 2d quantum transport relations everywhere except for a quantum greyhole in its center. Within the greyhole at the center of this universe, space itself does not exist, such that the question “what happens to quantum excitations that propagate into the greyhole?” has no answer in terms of 2d quantum transport theory (aka, 2D quantum field theory).

Fortunately, the laws of thermodynamics and causality are respected by the universe as a whole. Within the restricted context of 2d quantum field theory, greyhole scattering effectively scatters pure states into mixed states… yet this can be only an approximate description of the universal system dynamics (because 2d quantum field theory is only an effective theory of system dynamics).

It’s evident that greyhole dynamics can be naturally extended to include (as a 2D effective field theory) the special relativistic dynamics associated to the Klein-Gordon equation and the Dirac equation. And it’s evident too that thermodynamical transport theory survives pullback onto immersed tensor-network submanifolds of the larger Hilbert space—with exponential gain in computational efficiency as a valuable engineering bonus!—such that greyhole physics need not postulate a Hilbert state-space of exponentially large dimensionality.

What’s *not* evident is how to extend greyhole models to encompass general relativistic dynamics, while simultaneously preserving both thermodynamical validity and special relativity. Perhaps there exists an immersed submanifold of Hilbert space that naturally accommodates the trinity of (1) symplectomorphic dynamical flow, (2) special relativity, and (3) general relativity?

In any case, we can comfort ourselves with Laszlo Tisza’s thermodynamic maxim of 1966, “It is a noncontroversial statement that thermodynamics is a theory in close contact with measurement. Yet the specific implications of this statement have changed beyond recognition since the formative years of the classical theory.” Today more than ever (almost 50 years later) we appreciate that Tisza was entirely right to recognize that thermodynamics is a theory in close contact with measurement.

And so we can comfort ourselves too with the Confucian maxim “The man who removed the mountain was he who began carrying away the small stones.” Very plausibly, it will take quite awhile to finish clearing away this mountain.

Conclusion: The study of greyholes, within the restricted context that quantum systems engineering provides, is (perhaps) one “small stone” by which we can sensibly diminish our mountainous ignorance of quantum blackhole physics.

Summary: What’s inside quantum blackholes, we don’t know. What’s inside quantum greyholes is a finite amount of stuff that has no space-time description, yet is thermodynamically, informatically, and causally consistent with an (effective) field-theoretic dynamics exterior to the greyhole that converts pure states to mixed states.

John SidlesSeptember 2, 2013 at 6:14 pmAs a further remark:

————-

Scott Aaronson asks “How would one check that the collisions at (say) the LHC are unitary, if one didn’t already believe that? (Again, I can give an “in-principle” answer, but would be interested in what people actually do or would do experimentally.)”

————-

One rather elegant check is to observe (a) the imaginary part of the forward-scattering amplitude and (b) the total scattering cross section. These two quantities are related by what particle physicists call “the optical theorem” (Wikipedia provides a good account), and in practice they are measured to pretty good precision in what particle physicists call “kaon regeneration” experiments (again, Wikipedia provides a good account).

In greyhole/blackhole physics the main challenge is measuring the total scattering cross section, for reasons that include (a) preparation of a pure ingoing-state may be computationally infeasible for greyholes (the greyhole ground state may be computationally infeasible to compute) and is physically infeasible for blackholes (there is no blackhole ground state), and (b) observation of all outgoing-states may be computationally infeasible for greyholes (relaxation back the greyhole ground state may require an exponentially long waiting-time) and is physically infeasible for blackholes (the Compton wavelength of the evaporating blackhole eventually exceeds any ab initio detector size/temperature).

Conclusions: In practical particle-scattering experiments, kaon scattering is advantageous in that the in-state and out-state particles are massive, such that the tricky infra-red/zero-temperature/light-cone divergences of zero-mass quantum field theory are more readily evaded. Greyhole models on a torus impose a topological infra-red cutoff that similarly may help to cure these infra-red pathologies, at the price of making in-states and out-states less simple to define.

John SidlesSeptember 2, 2013 at 8:14 pmOh, and one final practical-physics note is that K0’s are massive *and* charge-neutral *and* spin-zero; otherwise they would possess electric and/or magnetic dipole moments that would introduce electromagnetic infra-red divergences into the scattering matrix; such divergences would (presumably) complicate and/or obscure the very delicate tests of time-reversal invariance that are associated to kaon-mixing experiments.

John SidlesSeptember 22, 2013 at 1:21 pmAnd yet another (powerful and in retrospect obvious) experimental check of the hypothesis “the quantum scattering matrix is unitary” is to observe the “BOSONsampling” statistics of the outgoing photons that are associated to Cerenkov and/or Bremsstrahlung radiation (Wikipedia has good articles on both).

These field-theory calculations aren’t easy even for simple bending magnets and beam-dumps; the scattering calculations become considerably harder — and the physics richer — for laser-like coherent x-ray photon emission from “wiggler” magnets, and the hardest-of-all unitarity/locality-sensitive field-theoretic calculations are associated to the highest-precision/lowest-energy physics of “g-2 experiments” in ion traps, in regard to which there exist, even today, plenty of unanswered fundamental questions that reside at the rich intersection of particle physics, condensed matter physics, quantum information theory, transport theory, and thermodynamics (for references, consult

e.g.the arxiv preprintsof Ford and O’Connell).John SidlesSeptember 4, 2013 at 9:39 amUpon further reflection, the relation between (TM-simulable) quantum greyhole dynamics and (our present understanding of) quantum blackhole dynamics includes the following features:

———————

(1) quantum greyhole dynamical flows are exact symplectomorphisms, and various conservation laws too can be exact; thus the Four Laws (of thermodynamics) are fully respected by greyhole physics at all times, and

(2) quantum greyhole dynamics can approximate relativistically invariant quantum field theories to arbitrary precision, and moreover

(3) quantum greyholes can include dynamically generated, spatially localized regions of “ylem” (see Wikipedia entries for Alpher and Gamow), within which the field-theoretic space-time models do not apply (albeit thermodynamics and causality still work globally), and

(4) dynamically generated event horizons can shield the ylem from external observation *except* during the final stages of greyhole evaporation, such that

(5) emission from “naked ylem” in the final stages of greyhole evaporation suffices to restore orthodox quantum unitarity and thermodynamic consistency to the aggregate greyhole model.

———————

Conclusion: In greyhole physics, the symplectomorphic dynamics associated to the visibility of “naked ylem” in the final stages of greyhole evaporation generically suffices (in principle) to resolve any-and-all all quantum unitarity and thermodynamic paradoxes. However, generic greyhole models are not particularly illuminating because so little is uniquely specified in regard to naked ylem dynamics.

John SidlesSeptember 19, 2013 at 11:56 amThe above greyhole examples show why — for quantum simulation purposes — it is natural for quantum systems engineers to regard Hilbert-space flatness, spatial locality, and scattering unitarity not as fundamental properties, but as emergent properties of simulation dynamics that generically is Kähler (rather than Hilbert), that generically is spatially localized by Lindblad/Onsager/Carmichael processes (rather than field operators), in which S-matrix unitarity is generically sacrificed (in that in-state and out-state dispersion is associated to an emergent notion of spacetime).

These same properties are attractive to particle theorists, and particularly commended is “Scattering Amplitudes and the Positive Grassmannian” (arxiv:1212.5605) and also Nima Arkani-Hamed’s lively lecture on the same subject

. In the former we read:The Amplituhedronand in the latter Arkani-Hamed comments (at minute 43:20)

These shared ideas — of gaining in both mathematical naturality and computational efficiency by sacrificing explicit quantum unitarity and spatial locality — are similarly attractive to 21st century quantum systems engineers as they are to 21st century quantum field theorists.

Wormhole Inside Blackhole – Quantum BotSeptember 3, 2013 at 6:10 am[…] … Black hole firewalls … firewalls again and again … Einstein-Rosen bridges vs Einstein-Podolsky-Rosen paradoxes … Finally, I […]

devhermitSeptember 5, 2013 at 1:19 pmLet’s entangle portions of matter. Use one portion to creating black hole and look what will happen to second portion.

???

Profit

Joe MarchioneSeptember 5, 2013 at 6:35 pmMaybe physicists just need to find a way renormalize the unknowable parts of this immensely complex interactive system and transform the paradox into its non-commuting complex conjugate … the finite anti-problem. Its way beyond me. : )

MartinSeptember 6, 2013 at 12:02 pmI there is a such think as a black hole.

pritishSeptember 9, 2013 at 7:18 pmWhere will all the laws and principles of physics fails???

What's inside a black hole? | Quantum Physics |...September 10, 2013 at 9:38 pm[…] I have a multiple choice question for you. What's inside a black hole? (A) An unlimited amount of stuff. (B) Nothing at all. (C) A huge but finite amount of stuff, which is also outside the black h… […]

ste vensSeptember 11, 2013 at 5:36 amI this is a really misterious fact that black hole are of a kind that has only darkness in it . . .Read more

kavehSeptember 21, 2013 at 10:44 amI don’t know the right answer but I am confident ADS/CFT duality is wrong , despite many publishrd papers in support of that.Indeed if we cann’t understand the ultimate nature of time,causality,space and evolution there is no hope to comprehendsingularities such as big bang and black holes interior .

CFTSeptember 22, 2013 at 1:41 amThere are no black holes unless you happen to live in a universe with only one mass. Last time I checked, we have at least a few more than one. Einstein’s field equations HAVE NO KNOWN SOLUTIONS for two or more masses. What this means is obvious, Black Holes are a mathematical fiction which only work in the framework of a mathematical space that in no way resembles our universe. Go outside tonight, if you see more than one thing up in the sky, you have just proven by direct observation you don’t live in a universe anything like what is required to generate a black hole.

Or you can do your homework.

“Black holes were first discovered as purely mathematical solutions of Einsteins’s field eqautions. This solution, the Schwarzchild black hole, is a nonlinear solution of the Einstein equations of General Relativity. It contains NO MATTER, and exists forever in an asymptotically flat space-time”

(Dictionary of Geophysics, Astrophysics and Astronmy; Edited by Richard A. Matzner, CRC Press LLC, Boca Raton, USA 2001)

I find it amazing that physicists dare mention Einstein’s name for credibility, then ignore the fact that his field equations are highly non linear and can’t have more than one mass in them at most. The mass they can put into the equations are actually not matter at all, but a fictional object called a singularity, which is an object of zero size, and thus has zero volume, unless you think multiplication does not somehow pertain to volume, or any other kind of geometry. There is no inside possible, unless you ignore logic and definition. A zero volume has no volume or inside to work with. Look up what volume means. Look up what interior means. Look up what a zero is. Look up the word ‘malarkey’.

John LawrieOctober 10, 2013 at 2:50 amD) None of the above, I think that black holes are in comparison to massive neutron stars only massive dark matter neutron stars. Material, as we know it, is sucked in due to the massive attraction forces. These are the greatest forces in the universe. Once the material enters the black hole it is ripped apart separating the atoms then converting them into new matter. Some of this new material is then spewed out into space as dark matter and helps to bind the galaxies and universe together. Of course, we can’t see the material being spewed out as the dark matter is invisible and can pass straight through ordinary matter as we know it. But it’s got to come from somewhere, Right?

sanjay soodOctober 10, 2013 at 4:07 pmHello Dr. Preskill,

I really enjoyed your latest post on Hawking radiation. I was wondering if you could explain the physical signaificance of the verticle solid line in the Penrose diagram.

MitelinOctober 13, 2013 at 9:27 amE) there is no black holes cause there is pleanty of other teories that actuali can be right. Nobody ever seen black holes onli some object that cud be described as maybe black holes but no prove. ergo black holes can be onli by product flaw of mathematic because we are stupid retaded monkey that fuking every time thing that we know everithing and every variable but in few year that proven wrong and new paticles and law are discovered and people start wild prediction abou universe again and again they sey we are absolutli sure … yea we know shit about universe and until we know more about what actuali is gravity fields time and what is in other spacial dimesions we shud fuck stop paying idiots making superior teories that every comon sence human know that will be in few years wrong !!! make our lives easier and dont fuck waste our money!!!!

HarriettNovember 2, 2013 at 11:14 pmHowdy! This blog post couldn’t be written much better!

Looking at this post reminds me of my previous roommate! He continually

kept preaching about this. I’ll send this post to him. Pretty sure he will have a

good read. Thanks for sharing!

Gil KalaiApril 2, 2014 at 10:35 amHi John,

Here is a speculation about the firewall black hole paradox. There is something problematic about the attempts (as beautiful as they are) to solve the AMPS firewall paradox using computational complexity. The fact that something is not efficiently computable does not mean that we do not have the information needed for the computation. (Harlow and Hayden mention in their paper various explanation around this but those are not so convincing.)

Since the issue is essentially about information and not about computation we may try to assume that the computation power (for everybody, Alice Bob, Charlie…) is unlimited, and only information is limited.

When we take this approach we need to pay a price: we cannot talk about closed quantum systems. For those everybody can compute everything from the initial conditions, and if we allow this type of computation the paradox (along with many other basic physical insights) goes away. What we can do is to talk about open quantum systems, namely to assume to start with, that we consider unitary evolution on a large Hilbert space where we have access only to a smaller subspace. (So this is the setting of noisy quantum evolutions.) And the small Hilbert space will represent a good chunk of the physical situation outside and inside the black hole.

I see reasons to hope based on standard assumptions on quantum noise that the black hole firewall paradox remains equally powerful (even with stronger informational foundations) for open quantum systems as well. (For example, we can send many Alices rather than one to overcome the noise, and we can take quantum computation for granted.) Maybe this is well known.

But perhaps conditioned on a

no quantum fault-tolerance principlewe have a chance to resolve the paradox . In particular, the hypothesis of positive correlations for information leaks for entangled subsystems seems relevant. If so, then in turn, we may gain insight on the quantitative aspects of this hypothesis. Note that my no-quantum-fault-tolerance conjectures are of information-theoretic nature and not of computational complexity nature.mohdonoJune 20, 2014 at 10:38 amblack holes for nobs

Mitru Costea 3rdMay 11, 2015 at 7:56 amThere is nothing inside a black hole. The gravity of the event horizon attracts both sides of the horizon leaving the interior as a vacuum LESS then that of “space”. Since the vacuum is lower, light cannot travel through it.

DavidJanuary 10, 2018 at 2:19 pmI searched many articles and blog posts but can’t find the exact definition of black hole. I read this post and found some useful information.