Singularities and Black Holes

Hawking, Thorne, and Naked Singularities

Posted by Jess Gates on August 30, 1998 at 12:04:36:

Re MEYER's comment: I posted down below that the properties of the singularity were not known, you told me that was not true.  But I haven't read anything in those references you put up to showme they are understood.

If I claimed that any aspect of of the physical world is completely understood, I should have my mouth washed out with soap, my tongue removed, or my (notoriously inept) typing fingers lopped off (and no, Helen, that's is most emphatically not an invitation . . . :-D). Many aspects of singularities of both types (cosmogenic; black hole) are well described by Einsteinian general relativity. In regions near/at the singularity itself, however, a  lot more undertanding is required of the relationship between general relativity and quantum mechanics. That's the reason that the quest for a quantum gravitational theory is so much in the news these days. Until that is accomplished (if it indeed can be in ways that physicists susect it can be), descriptions of singularities will fail at very high densities.

In particular, quantizing gravity will require an understanding of what happens at energies (temperatures) far higher than our most accomplished accelerators currently probe. A one of the "Ask the Astronomer" answers (below) indicates, there is some reason to believe that within spacetime regions near the Planck length (10-33 centimeters) and Planck time (10-43 seconds) the singularity will be "smeared' by quantum effects into a region where the density approaches 1094 grams/cm3. while this is a very high density, it would avoid the inifinities that currently plague existing GR characterizations of singularities.

 

Re Lucas' response to MEYER: I don't know what you're babbling about...The universe began with a singularity. It wasn't a black hole.I don't think that MEYER is babbling; I think that he's trying to understand. From his past statements I infer that, like me, he comes to this discussion with an imperfect (in my case, virtually missing) grasp of the mathematical underpinnings of general relativity and quantum mechanics/QFT. I havene't even figured out what a Bogliubov transform is yet.

MEYER, one of the problems you seem to be having is that you have inferred that all singularities are black holes. This appears not to be the case. See If the Big Bang singularity dwarfed a black hole singularity, why did anything ever escape? which says

"Because it was a very different kind of a singularity than what you find inside a black hole. The essential physics were entirely different. There were no 'in-going' geodesics, only 'out-going' ones in time. For black holes, you only have 'in-going' geodesics. Also, black hole 'solutions' are part of the local geometry of space-time and are embedded objects. The Big Bang singularity is part of the global geometry to space-time and is not an embedded object. As to how matter escaped from the Big Bang singularity, it's simple. Matter had no choice. These were the only geodesics possible at the time.  Also, although local 'horizons' were present, they were constantly growing in size so that today they have all merged together to form the one that we see as the horizon to the visible universe."

You may also want to look at Why wasn't the Big Bang a black hole?, which notes in part

"Some people have noted the parallel between the 'singularity' at the Big Bang out of which the universe andspace-time emerged, and the singularity within a black hole. Since matter and energy emerged from the BigBang singularity, it bares some resemblance to the so-called 'white hole' solutions in general relativity, which are time-reversed versions of black holes in which matter/energy are continuously being emitted rather than gravitationally attracted. In the Big Bang situation, this parallel would require that we live inside the event horizon of the cosmological singularity. The problem is, again, one of exterior spaces. Einstein's field equation describing these white hole solutions still requires the pre-existence of an exterior space-time withinwhich this white hole singularity occurs. The Big Bang solution does not presuppose the existence of an exterior space-time in which the entire space-time that makes up our universe came into existence. Thesolution itself merely describes the unfolding of space-time from this incomprehensible Cosmological Singularity which is, mathematically, of a different class than any black hole or white hole singularity."

This and other answers from Sten Odenwald's "Ask the Astronomer" site are attempts to explain in layman's terms the arcane mathematical models that descrbe both the cosmological singularity and black hole singularities. Don't expect them to "explain" in any coherent sense that which cannot be understood without recourse to heavy-duty math. Odenwald is, however, pretty good at coming up with analogies to make things more-or-less understandable to Philistines like myself.  Other answers at "Ask the Astronomer" that might be of interest to you are"

  • Why is the Big Bang described as a singularity when Einstein himself said that physical singularities do not exist?
  • If the Big Bang started out as a ball of compressed matter, why do some objects now rotate clockwise and counter-clockwise?

One (probably naive) way to look at it is this: the Big Bang was a rapid expansion of spacetime, while black holes are localized regions of highly curved spacetime within larger regions of relatively flat spacetime.

BTW, I think that Odenwald tries very hard to explain astronomy, cosmology, and astrophysics to general audiences. In fairness, however, you should be aware that he has little tolerance for folks who try to force-fit creation mythology into scientific paradigms. Note, for example, his response to Do you believe in the Big Bang theory, or Creation?, which says in part

"Do I 'believe' in the Big Bang theory? If the comparison is between one methodology that respects contraryevidence ( the Scientific Method ), and one that suppresses it and is based on ridicule, political intimidation, and a deceitful use of evidence ( the Creationists approach ), I believe that the scientific story is far more accurate as a story about the physical world. Among western biblical scholars, those individuals who actually take the time to look critically at the Bible, there is unanimity that the scientific story is not at all in conflict with Genesis. Even the Pope accepts Big Bang theory as a fleshed-out description of God's handiwork!

If you now argue that Big Bang theory is just a theory and that all  theories are not proven fact, then you have just reduced all of science to some kind of silly passive process of recording events with no meaningful certainty in interpreting them. This is, of course, a meaningless quibble which many people have difficulty with, especially those vocal few who wish to insert Creationism into our schools as an equally scientific 'theory' of the beginning of the universe. Their proposal for 'balance' falls on receptive ears because who would not want the process of investigation to be a democratic one with all voices respected for their views.  The problem is that the advancement of science has nothing to do with  democracy or with what feels good and makes sense. Quantum mechanics and relativity don't make much sense to anyone, and relativity certainly doesn't make anyone feel good. Like the slogan on the T-shirt says " The speed of light is not just a good idea, it's the LAW". "

Given this opinion, Odenwald's theology may be suspect from the standpoint of "scientific creationists" of either the "young earth" or "old earth" ilk. However, he does seem to try very hard to communicate science to a wide range of readers.

On the "information loss" problem (discussed by Lucas and  Helen)

This "problem" relates to what Hawking and others have termed the "no hair" theorem (i.e., "black holes have no hair"). I will not attempt to define the term "information" here in any technical way, since I am unqualified to do so. Some aspects of the "information loss" are, however, relatively easy to understaqnd. As entities, black holes can be completely described by three properties: mass, charge, and angular momentum. But the "information content" of the entities that enter the event horizon is much larger. One might dump the Encyclopedia Britannica into a black hole, for example, and the "no hair" theorem suggests that all of the organized information in that set of books would be lost to external observers for all time. This is a trivial example of "information loss".

There are, however, more basic aspects of "information" that would also be lost if the "no hair" theorem is correct. Mass/energy at the most basic level is characterized by several "quantum numbers" or "characteristics", and the "no hair" theorem implies that much of the information about even individual particles is lost when they enter the event horizon. Baryon number, lepton numer, strangeness, colour charge, etc. all disappear behing a "wall" from which escape of information is prohibited by the characteristics of black holes as (and to the extent that) science understands them.

There is another "problem" that deals with the status of the observer entering the horizon of a black hole. Most discussions of information and entropy associated with black holes are made from the viewpoint of a distant observer (one at an infinite distance form the BH, or one in relatively flat spacetime at a fixed distance (usually large) from the BH. As infalling material enters the event horizon, distant observers can get less and less information about the state of that material because the electromagnetic radiation that communicates that information gets more and more redshifted. Here things get a little fuzzy to me, because we now enter a realm with which I am somewhat familiar --- communication in noisy channels, which is described by the work of Shannon. basically, Shannon's law sets an upper limit on the amount of information that can be communicated as a function of signal strength (energy per binary digit [Eb]) and noise power spectral density [N0]. The ratio Eb/N0. Since Hawking and Bekenstein demonstrated that black holes do radiate, at some point near the event horizon the information that one can derive from observing (or communicating with, for that matter) material entering the BH event horizon gets swamped by the Hawking radiation --- in other words, the Eb/N0 gets so small that the amount of information transfer is quite limited.

Eventually the material crosses the event horizon, and Eb drops to zero: no information gets out.  Now consider an observer carrying a set of encyclopedias and a small but  powerful physics lab into a black hole. If the BH is sufficiently massive such that tidal effects at the event horizon do not  rip the observer to pieces (and this is quite possible, BTW), the infalling observer does not notice anything dramatic. S/he switches on a flashlight and reads the encyclopedia; s/he performs experiments that distingish the quantum states of particles in the immediate environment. In other words, the universe looks largely as it did before s/he crossed the event horizon. So we have two different observers with very different perspectives on the information content of stuff inside the event horizon of the BH. In a sense this doesn't matter, because once the infalling observer crosses the EH two things occur: (1) s/he an no longer communicate anything to the distant, "fixed" observer, and (2) s/he is doomed to encounter the singularity at some point, since within the event horizon all world lines (geodesics) lead to the singularity. (I ignore here the case of rotating Kerr BHs with "disk" or "ring" singularities; some interpretations would allow the infalling observer to survive this experience).

It should be noted, however, that not all theoreticians believe that the "no hair" holds completely. In the Hawking/Penrose discussion referenced below, for example, Penrose argues that at least some of the information "lost" at the event horizon will be recovered during the process of BH evaporation. Other theorists (most notably string theorists) feel that to a distant observer all of the quantum information associated ith infalling material is "stored" as strings at the EH. There are more things in heaven and earth, Horatio . . . .

Re Joe martin's comments (several, reproduced in bold italics)

"[To Lucas]: Your understanding is silly. "

It didn't look silly to me. With what aspect of Lucas' comment did you have a problem??

"Virtual quantum particles at the event horizon of a black hole are composed of matter and antimatter. They cannot exist together."

My (limited) understanding is that they always exist together for that brief time interval permitted by quantum and relativity theory. It is true that real (not virtual) particles pairs will vanishin a blaze of gamma radiation, but virtual particle pairs are very different from real particles. The gravitational and electomagnetic effects of BHs are, for example, mediated by virtual particle interactions, not real particle interactions. You seem to be confusing the two.

"They are dimensional opposites that exist in two different realities."

Do you have any substantiation for this assertion? As far as i know, matter and antimatter when manifested as real particles are very much a part of the universe that we know about; there are not "separate realities".

"The antimatter falls into the black hole and the information is lost to our dimension. The matter particle is released into our dimension, (Hawking radiation)."

I don't think this is the case. For charged black holes, it would appear that a BH would preferentially emit particles or antiparticles of the same charge as the net charge of the BH (i.e., the BH would "prefer" to reach charge equilibrium). For uncharged black holes, whether the partcle or antiparticle memeber of the pair was "emitted" would alrgely be a matter of chance (unless antimatter has a negative "mass charge", whcih does not seem to be borne out by either GR or experiment [though the experimental evidence is none too compelling at the moment, admittedly]).

"There has been an exchange of information from the natural and the supernatural."

Again, I would like to see some scientific substantiation of this claim. What physicist do you know of who talks about positrons (which are routinely observed in accelerator events) as "supernatural"?

"The question is whether or not it accurately reflects the empirical evidence and how much the brain can effect that evidence. Quantum reality is such, that our brains do indeed effect that evidence. Simple enough for you Lucas?"

It looks as though you have bought into some version or other of the participatory universe interpretation of QM.  Since Wheeler was heavily involved in the development of this interpretation, I suggest you read what Wheeler has to say about folks who have used his ideas to promulgate myticism.  There are many interpreatations of the "deeper meaning" of the seeming paradoxes of QM, but they all use equivalent math come up with the same physical answers. I have heard it said that most practicing physicists don't worry too much about the philosophical aspects of QM interpretations that attempt to grapple with the classically contrainutitive aspects of QM. Mostly, they do the calculations that provide the answers they need.

 

 

 

 
 
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