Evaporating Black Holes

by Robert G. Hays

Some Notes On The Evaporation Of Black Holes

by

RGHays (Robert G. Hays)

7/30-31/1988.

(Note: Earlier today I started hunting in my Funk & Wagnalls encyclopedia for information on medical magnetic resonance imaging. In following the various leads from that article I wound up at the entry for black holes, and that article [finally] brought on and together the following thoughts. RGH)

(All of those who will be interested in the following will doubtless already be familiar with the terms and ideas that I will be using here, so I shall predominantly refrain from basic descriptions. RGH)

Please treat any words in ALL CAPITALS as being in *italics*.

Some time ago Stephen Hawking proposed that "primordial" black holes may have been formed at the time of the 'Big Bang.' He also proposed that any of these primordial black holes of less than approximately 1,000,000,000 metric tons original mass may have 'evaporated.' The mechanism that he suggested to cause this evaporation involves the spontaneous electron-positron-pair generation from high-energy radiation.

In this view, one member of such a pair that formed at or near the Schwarzschild radius might fall into the black hole, while the other escaped into space. In this paper I am going to examine this to show that such a mechanism would not cause ANY black hole to evaporate.

For the first and primary case I am making the assumptions that:

1) all acceleration is linear, i.e., not in quantum units;

2) gravity does not have a propagation velocity;

3) electron-positron pairs form at approximately zero separation;

4) time is 'smooth' (but this is largely irrelevant);

5) that the anomaly has a three-dimensional size of zero -- again largely irrelevant, as the 3-d size will always be (proportionally) far less than the Schwarzschild radius; and that

6) matter, electromagnetic energy, and nuclear forces are all a form of mass (MASS), and gravitically may be treated the same. These are the currently best evidentially supported assumptions. For other cases, please see the separate discussions below.

As a clarification, I will note that the the ACTUAL PHYSICAL black hole -- which is called the ANOMALY -- is by definition a geometrical point at the center of the Schwarzschild radius, and that the Schwarzschild radius is NOT the boundary of the PHYSICAL black hole, but rather IS THE (SPHERICALLY RADIAL) DISTANCE FROM THE ANOMALY AT WHICH THE (GRAVITATIONAL) EFFECTS OF THE BLACK HOLE BECOMES SO POWERFUL THAT EVEN ELECTROMAGNETIC RADIATION CAN NO LONGER ESCAPE, NOR CAN ANY FORM OF MATTER TRAVELLING AT LESS THAN 'C.'

(The distance from an auto-lifting magnet at which it can no longer pick up a dinner-knife is a usable analogy here: that distance could be considered the "Knifegrab radius.")

Since the definition of the Schwarzschild radius is that of being the distance at which no conceivable (quantum or otherwise permissible) mass existent can fail to be drawn into the black hole, and that the gravita- tional effects of the black hole must by definition be proportionally stronger at lesser distances from the anomaly, said mass would have to escape even stronger gravitational forces than what any mass can escape in order to get to the limit -- which by definition it still cannot escape -- to be able to radiate away into free space, where it WOULD represent a loss of mass from the black hole.

From the above then, it follows that any mechanism occurring INSIDE THE BLACK HOLE that produces matter or electromagnetic radiation cannot result in a loss of mass from the black hole. I.E.: even granting through quantum mechanical effects that some mass product might actually (momentarily) escape the anomaly -- any such product would still have to traverse the distance from just outside the anomaly to the Schwarzschild radius, which traversal is impossible, as by definition said product would be rapidly drawn back into the anomaly.

Which leads to the next point, namely that any electron-positron pair that formed AT THE SCHWARZSCHILD BARRIER must of necessity come from quanta of energy that was INBOUND TOWARDS THE ANOMALY, and which was thus due to add its ENTIRE quanta to the mass of the anomaly, AND THUS IF ANY PART OF THE INBOUND QUANTA FALLS INTO THE BLACK HOLE IT STILL REPRESENTS AN ADDITION TO THE MASS OF THE BLACK HOLE.

The suggestion has also been made by someone that perhaps the reason that the universe is composed PREDOMINANTLY of "normal" matter is due to some as-yet-undiscovered mechanism by which most or all of the time in such pair-production, it is the 'antimatter' component which is captured by the anomaly. Some might offer the argument that the black hole is being evaporated by this particular factor.

The answer to this is that:

1) Antimatter still (from the argument) responds "positively" to gravity (else it would promptly exit the black hole, and essentially follow the 'normal' particle), therefore it stands proven that antimatter mass would still ADD to the anomaly's mass, so long as it remains in the form of "matter"; and that

2) if a primordial (or other) black hole were formed (mostly) of 'normal' matter before this infall began, and the matter and antimatter particles still collide, resulting in their mutual 'annihilation,' which is only their reversion to the 'energy' form, said resultant energy could still not escape the gravitic field, and given that matter and energy are two forms of the same thing, the mass still remains, only its 'nominal' (and probably irrelevant) form has changed, thus the infall still adds to the mass of the anomaly.

I must add here that at the present time there is no reason to suspect that the area between the Schwarzschild radius and the actual anomaly is in any way special other than that any mass "found" in this area is always inbound into the anomaly.

Clarification: per general relativity, and also (most of) quantum mechanics, if any mass were to reach the velocity 'C' its mass would INSTANTLY become INFINITE. INSTANTLY in quantum physics means IN ZERO TIME or IN THE SMALLEST UNIT OF TIME THAT EXISTS, depending on which theory of time one chooses to consider true. In the latter case, this means IN THE SAME UNIT OF TIME IN WHICH THE MASS'S VELOCITY EQUALS C. INFINITE MASS would also have INFINITE GRAVITY, thus THE ENTIRE UNIVERSE WOULD BE DRAWN INTO THE FIRST BLACK HOLE AT WHICH THIS HAPPENED.

Since the fact that from the beginning of the universe there has been radiation of some kind (big bang = *S*O*M*E* *K*I*N*D*), then from the first moment that a black hole existed anywhere in the universe, it had mass falling into it.

Which last two paragraphs, combined with the fact that a gravitic field from within the Schwarzschild radius DOES effect the 'outside' universe, prohibit infalling mass inside the Schwarzschild radius from exceeding C, if the 'big bang' and the 'primordial black hole' theories are both true. If the 'steady state,' 'big bang'*sans*'primordial black hole,' or some third (ad infinitum) theory, then the question becomes when did the first black hole come into existence? I pass this one for now: see next para.

In fact, if the theory about infinite mass meaning infinite gravity is true, and infalling (anomaly) mass can exceed C, the question is just exactly what happens to the entire universe once this velocity is reached?

The final (derived) answer to this is that on the first occurrence of mass-at-C the entire universe becomes a black hole, and, due to the fact of being within a Schwarzschild radius, and thus reaching C, once all matter in the universe reaches C -- which it instantly does -- all time frames come to a complete stop relative to all others, and since for each vector towards the first mass-at-C black hole there is another timeframe, all time-dependent processes in the universe -- which is all processes -- stop.

Please note that this all happens by definition INSTANTLY, thus the consideration of what happens when the first infalling mass travels FASTER THAN C is irrelevant -- it never gets to.

Since the universe is obviously not stopped -- or else I could not be writing this! -- we must give up one of the following: black holes, infinite mass means infinite gravity, gravity-as-propagated-wave-with- real-velocity & gravity-as-acceleration & gravity-as-instant-effect-on- fabric-of-universe, or mass-inside-Schwarzschild-radius-exceeding-C.

I choose to drop the last: it already apparently contradicts too much.

Black holes not existing? Possible.

The Infinities? Possible, but TOO many contradictions, I think...

Propagated-wave? We still could not see -- at any wavelength INCLUDING X-RAYS -- a black hole; the moment we see ANY effect, we are faced with the fact that said effect was not captured by infinite gravity -- else it couldn't get here. (Actually, we could see something: a spherical x-ray source that would grow at the propagation velocity of gravity -- we would be seeing the x-rays from just outside the Schwarzs- child radius.)

Acceleration? See above -- all time frames at once or wavefront, but still one of the above.

Of course, 'instant gravity' is the main case that I started with.

And I ask you to note that I have covered 'bumpy' time in the paragraph above starting off "Clarification: ..."

Adding my previous point about mass escaping THE ANOMALY, which means that all inside-Schwarzschild mass is inbound, we arrive at the conclusion that I already stated: "... there is no reason to suspect that the area between the Schwarzschild radius and the actual anomaly is in any way special ...".

I went on in that quote to say that all mass in "... the area between ..." must be infalling. Why? Observe: if, due to the above considerations, mass/energy cannot exceed the speed of light, then this must also be true of mass "attempting" to leave the black hole. I.E.: the infinite gravity clause which prevents (our thinking that) infalling matter is allowed to exceed C applies to ANY matter in this zone (or anywhere in the entire universe, for that matter). Since the proof lies in denying mass to reach C in the first place, no mass IN ANY FORM can exceed C, and thus cannot escape the gravitic influence of the anomaly, and thus can never escape.

INSTANTANEOUS transition to above-C? By almost all theories this means traveling BACKWARDS IN TIME. Thus said mass will have to re-trace -- going back in time -- its entry into the Schwarzschild radius. Now, once it has gotten out, does it continue to travel backwards in time? If not, then when it reverts to 'realtime,' it will immediately fall in again. For all gravitic purposes to the remote universe, it is still trapped by the black hole, and its mass still pulls anything REMOTE in the same direction.

I am NOT getting into the insanities of "mass traveling in direction X going backwards in time equals mass traveling in direction -X going forward in time": this would have to mean that any mass ESCAPING FROM the black hole ADDS TO THE MASS of the black hole.

Yes, it continues to travel back in time once it is out? There is some slight evidence to INDICATE -- indicate, NOT prove -- that THAT is what anti-matter is: matter traveling backwards through time, thus while the black hole does diminish, the universe gets filled with antimatter, which does not appear to be the case, so either this is EXTREMELY slow, or it is entirely false at some point. I will concede that this particular mechanism MAY evaporate black holes, but I doubt it: the observed radiation from these (suspected) areas does not support this. (Of course, most of the antimatter would collide with infalling normal matter immediately, giving rise to certain extremely high energy radiation which has been observed in the laboratory. It is not present around suspected black holes.) (At least, researchers believe that that is what they have observed; if not, then a lot of physics is in error, given the process by which the judgement of what has been seen has been reached...)

Mass is instantaneously converted to velocities above C without traveling backwards in time? THIS IS POSSIBLE, and if true is the only mechanism which could 'evaporate' a black hole. It is also the probable source of any tachyons that may exist. Tachyons are presumed to have no mass at rest (or at sub-C velocities), or even to have negative mass, which last, considering how 'exotic' must be any process that can so transpose the energy level of mass, could also be a result of such a process, or even THE result of the process, and the CAUSE of the trans- light speed.

There is another probable problem with this last assumption. I will postulate (sans any evidence) that due to quantum effects, or unknown, the only form of mass that is allowed to exist AT C is the photon (and perhaps the graviton), while MATTER can exist on BOTH SIDES of this barrier. We are still left with the question of just how close to C is the quantum limit for MATTER? Presuming from the laboratory that the limit is some quantum (small) amount, we still have the mass-expansion factor to contend with, and when remembering that there will be a LOT of mass falling into some of these anomalies, the gravitic field may still become large enough to convert the ENTIRE universe into a black hole.

I think that any direct form of quark interaction will prove to be covered by one or more of the above arguments. This should also go for any other currently-known form of mass.

Neutrinos? They are still 'real-matter' particles, with mass, traveling below C. Or else we may treat them as photonic mass.

(From the previous definition of the Schwarzschild radius, also known as the 'event horizon,' it can be seen that there is NO POSSIBILITY within the currently-known laws of physics of ever encountering a "naked singularity." ('Singularity' and 'anomaly' are of course the same thing.) (I prefer 'anomaly' because there is more than one, and they are [apparently] associated with anomalous behavior, beyond sheer mass and gravity.)

There remain three interesting questions which I feel currently qualified to discuss, if not to solve.

The first is, given the quantum step 'around' C inside a black hole, what happens if the velocity vector points along a chord of the radius? Does the mass still escape, perhaps after one or more orbits? Also what if the vector points DIRECTLY at the center of the anomaly? Does this come out of a white hole? (Or even this and only this?) What happens if it does not? Could this collision cause the destruction of the anomaly? Or simply cause more mass to be accelerated (perhaps in several vectors)?

As to the chord, I pass: the mass may have become tachyonic, and so may be gravity-negative; or the velocity may produce a curved or straight line leading out of the anomaly or Schwarzschild radius, possibly still falling back in, or it could become a spiral or stable orbit. In short, I, at least, do not have enough data or useful definitions to attempt to answer this one, nor to do more than point to possibilities.

I will further question one point though: if the result is a spiral or stable orbit, whether or not said spiral eventually ends outside or in the exact center, what other effects will the orbiting mass++ have within the black hole? Curious possibilities.

Directly at the center is similarly complex: there is yet no reason to suspect that 'white holes' do in fact exist, but neither that they CANnot; what further acceleration the mass would undergo, if any, is also open to debate and data, or it could 'bounce' several more masses out. This one seems reasonable: mass in particle form is still particles, which observably do bounce (gas pressure, plasma, &c &infin.). I do think that the possibility of such a vector causing the destruction of the anomaly is UNREASONABLE: given the amount of massES inside the Schwarzschild radius (at least in an intra-galactic black hole), this would have to happen fairly constantly, thus no x-ray-emitting black hole would last more than a short time (probably measured in hours or minutes). (Remember that the x-rays come from the acceleration of the infalling mass OUTSIDE OF THE SCHWARZSCHILD RADIUS in the accretion disk, which means that there is a CONSTANT FLOW of infalling mass into the black hole.)

Note that in all three of the above paragraphs the processes mentioned probably are still quite slow, although such data as yet exists could be re-interpreted fairly easily by my current knowledge of how much we know.

The second interesting question has to do with just exactly what happens to mass once it falls into a black hole, and perhaps this is two questions: one at the event horizon (Schwarzschild radius), and one at the edge of the anomaly (if it has one, which seems likely). Does this mass get forced into one of the known forms: photons, particles, neutrons-in- particular, quarks, &c? If particulate masses can exist inside a black hole, do they retain ANY three-dimensional size? Translated into other (physical) dimension(s)? (This last also applies to photonic mass, if allowed; so does the next.) Sent (instantly) back to the beginning instant of time (I.E.: The Big Bang)? Which last COULD indicate that the universe is looped on itself: this COULD be the CAUSE of the Big Bang!

This still probably does not indicate whether the universe is open or closed, curved or flat, finite or infinite, and it does require some VERY exotic quantum laws to preserve causality, or rather in this case, to BE causality. It also could imaginably go back through several oscillations, but this would make that theory unnecessary. (It was originally proposed as an answer to the question "Where did the Big Bang come from?," and only later was the reverse-and-return of the present universe accepted as indicating the 'cyclical-bang' theory.)

(I have long favored the steady-state theory as most likely, if not most 'elegant;' this last 'return-to-start' idea just occurred to me sitting here at 3:00 am... It does present a point where the two theories meet, and may allow the retention of the facets of each which seem to be supported by observational evidence. But as I said, it would not BY ITSELF answer whether the universe will 'survive' or not.)

(I note that the whole possibility of 'virtual particles' which DO have a (probably short) PHYSICAL EXISTENCE narrows the gap between the two theories; it IS the first step in a mechanism that COULD in theory provide for a 'steady-state' universe. No, I am not overlooking the matter- antimatter question, but some similar mechanism, possibly including anti- muons or similar particles, could meet the conservation requirements, while only producing long-lived 'normal' matter. Also worth some observation is the issue of producing quark-antiquark pairs: 'normal' matter by current definition includes antiquarks as a matter of course. And then we still have to completely discover and define the interactions of leptons and quarks. Et cetera. And I present it here for thinking on, not as an attempted solution, nor even particularly as a theory yet.)

As to what happens, and what is ALLOWED inside a black hole, I pass. I can raise the questions, but again, I know too little to suggest an answer.

The last question is whether the universe is IN A BLACK HOLE, and if so, how can black holes exist inside of a black hole?

I start with the background (microwave) radiation. While the background radiation is used as one of the main pointers to the truth of the big bang theory, it could also be some result of infalling mass, or part of the sometimes-mentioned 'fabric-of-space' stresses within a black hole.

As to the sub-question of black holes inside of a black hole, this would seem possible, at least in the zone inside of the Schwarzschild radius and outside of the anomaly.

Next comes the doppler effect, which means the apparent EXPANSION of the universe. Again, one answer inside a black hole is 'fabric-stress.' Another is that the closer one gets to the (center of) an anomaly, the higher the gravitic acceleration; thus 'further-in' sources of light would be reddened by their higher velocity 'in,' while the light from 'further- out' sources would be reddened by OUR higher velocity 'in.' As to light from 'beside' us, the nearer sources SHOULD appear blue-shifted (check the 'true' and 'apparent' angles, and actual 'line-of-flight'), thus the unbroken red shift would SEEM to disprove this, at least given that the universe became a black hole longer ago than would be required for the light to reach us from these 'broadside' sources. That time, of course, is part of the definition of 'nearer.' For further 'broadside' sources, the angles and flight-lines and gravitic effects make the data questionable.

For the gravitic part of this question, I think that since the acceleration 'in' would ESSENTIALLY be the same over the entirety of so (relatively) small an area as the solar system, or even the reliably, orbital-velocity measurable portion of this galaxy. As to what we can observe of orbits from further out, while this light has been delayed, and is thus old data, it still points to the idea of a 'free' universe, by essentially the same arguments as the doppler shift.

So does the 'quasar' question from all edges of the universe, the ALL EDGES factor being that which points away from a 'trapped' universe. I.e.: the light from whichever side is on the other side of the universe from the black hole would not get here at all, or, due to gravity-doppler, would appear from FAR to SOMEWHAT more red-shifted in a widening circle around the line from us to the central anomaly, and would generally tend to provide fainter, blurrier images the closer the visual angle to the object came to the line straight at the anomaly. This effect would be least straight 'out' from us, or behind us from the anomaly's "point of view," and would increase in a circle from there to 90 degree, and on to looking straight towards the anomaly, by which time the images are SEVERELY red-shifted, or missing, age-since-anomaly-formation depending.

From the above reasonings, I think we are NOT inside a black hole, but I do not claim to be able to prove it (yet, anyway).

All of these questions want answers, and all of these answers are going to be slow and difficult to acquire. Some of them we may never know, although I much doubt this. At least one of these questions is extremely interesting cosmogonally, and also philosophically.

Of course, the reason that I chose to discuss these latter questions is their relationship to the central point of the paper: that black holes (extremely probably) do not 'evaporate,' and by what processes they would if they can, and thereby to lightly suggest the correct directions to research to settle the whole question. The first question, vectors, relates obviously to evaporation. The second, what is allowed, again relates directly to this question. The third was required if I was to attempt ANY completeness of the fact that we are not inside of a black hole -- or at least not one of the same order and rules as those we observe, which would bring into question whether it should be called or THOUGHT OF as a black hole -- which relates to evaporation through trans-C velocities and infinite mass/gravity.

Where I consider myself to have insufficient knowledge to reason from, I have refrained from comments, and instead only pointed to the questions that I could see; where I think I do have a useful amount of knowledge, I have tried to point at the answers as I see them, but some of these views have changed as I acquired more knowledge. All are subject to change on that basis. The requirements of reason are the only invariable here. Again I state: I am not connected with physics except as a layman who tries to follow the subject when he can make the time to do so in.

The main reason that I wrote this is the pleasure of working all of these problems out, starting from one of my higher interests, and on a point where I realized that the theory being offered to me appears less than entirely logical, from the definitions of the existents involved. Definitions change and expand, and if they prove wrong, they may even be approximately reversed. One does the best one can with what one has.

Still, I am pleased with this paper, and I think that more than a little of what I have said here may eventually be PROVEN correct.

(Beyond the enormous satisfaction of doing this paper, I even had a little impromptu fun: my description of the big bang, and the analogy "Knifegrab radius," both of which were very useful underlinings of the points that I was making, and both were selected by that criterion, but both were also kind of fun.)

I hope the reader gets the same pleasure in studying this paper, and in following it up, that I have had in writing it.

I do not get on CompuServe very often, but I will try to check back soon. Also, I am including my mailing address for those who might wish to correspond (if any). I will TRY to answer any interesting mail rapidly.

RGHays.

Robert G. Hays

3421 Fox St. C3

Duluth, Ga. 30136

(Looping causing big bang: stellar ignition has never been fully right: why not push all away before full? (Super)Nova blast = momentary over- mass causing blowback through time of core fraction causing ignition??)