merrill@rex.DEC (12/10/84)
If the whole universe was ina speck, said spec would have been a black hole and the "big bang" could not happen. No one has yet disputed this. Why not?
jlg@lanl.ARPA (12/11/84)
> If the whole universe was ina speck, said spec would have been a black hole > and the "big bang" could not happen. No one has yet disputed this. Why not? The whole universe was not (necessarily) in a spec. The density of the universe was very high. All of the universe that is presently visible (radius of about 15 billion light-years now) was once compressed into a VERY small space. However, high density does not cause black holes - high gravitational curvature does. Let's take a few examples: 1) Assume an infinite universe with uniform, but very high, density. Since the universe is infinite, it is radially symmetric around any point. Any radially symmertic region has a gravitational field of zero in the interior of the region (any physics 200 level course will force you to work out infinite variations on the proof of this fact for any inverse-square force ad nauseum). Therefore the gravitational curvature within this universe is zero everywhere - regardless of the density. (Now start stretching this universe uniformly in all directions and you'll have a 'big-bang' effect.) 2) Assume a finite, unbounded universe with uniform, but very high, density. Since it's hard for most people to visualize such a thing, consider the surface of a sphere. The surface of the sphere is radially symmetric around any point. A sphere's surface is a two dimensional object which is curved in the third dimension; the three dimensional analog of this curved in the fourth dimension is an example of a finite, unbounded space. As on the sphere, the 'hypershpere' is radially symmetric around every point, and by argument (1), the gravitational curvature is everywhere zero. (Now expand this universe uniformly in every direction, like increasing the diameter of the shere, and you again have a 'big-bang' effect.) 3) Assume either an infinite or finite universe that is at least VERY LARGE (this means at least large enough for the following scenario). Assume that the density is not uniform, but is VERY high in one region and low elsewhere. If the density of this universe declines gradually as function of the distance from the center of the high density region, so gradually that the gravitational curvature nowhere exceeds the Swartzchild limit, then no black hole will form. Since the properties of such VERY dense matter are not well known, this dense region may start to expand into the surrounding space (due perhaps to nothing more complicated than pressure). Well, there are three possibilities. None of these imply a primordial black hole, and all of them lead to the possibility of an expanding universe. Which of these (if any) is accurate is a subject for controversy, and there may be other explanations which are just as good.
wkp@lanl.ARPA (12/11/84)
> If the whole universe was ina speck, said spec would have been a black hole > and the "big bang" could not happen. No one has yet disputed this. Why not? I don't know why not (that's why I read net.religion). The answer to your question is quite simple, though it is a very good question, and quite profound. The answer is that the matter in your speck never crossed the "event horizon" of the universe, i.e., it never escaped from the black hole. First thing you need to do is to estimate the Schwarzschild radius for the universe, R = 2GM/(c**2). In this equation, M is the mass of the universe, G is the gravitational constant, and c is the speed of light. Estimating the mass of the universe in the usual way, one finds that the Schwarzschild radius of the universe is of the order of a GigaPc (10**9 Parsecs). Since this radius is much larger than the aforementioned speck (and the present radius of the universe), one concludes that the big bang can easily happen since the mass of the universe is still within the "black hole" radius of a Giga-Parsec. Of course, this means that we are all living within a black hole, and that nothing in the universe can travel outside our own Schwarzschild radius of 10**9 Parsecs. This question has been dealt with in the literature a number of years ago. If there are a lot of requests, I can scrounge up the references. bill peter los alamos
jin@hplabs.UUCP (Tai Jin) (12/11/84)
> If the whole universe was ina speck, said spec would have been a black hole > and the "big bang" could not happen. No one has yet disputed this. Why not? perhaps it reached critical mass and exploded? :-)
sharp@noao.UUCP (Nigel Sharp) (12/11/84)
> > If the whole universe was ina speck, said spec would have been a black hole > > and the "big bang" could not happen. No one has yet disputed this. Why not? > > The answer is that the matter in your speck never crossed the "event > horizon" of the universe, i.e., it never escaped from the black hole........ > > Since this radius is much larger than the aforementioned speck (and the > present radius of the universe), one concludes that the big bang can > easily happen since the mass of the universe is still within the > "black hole" radius of a Giga-Parsec. > > Of course, this means that we are all living within a black hole, and > that nothing in the universe can travel outside our own Schwarzschild > radius of 10**9 Parsecs. > > bill peter > los alamos Oh dear me no ! Over and over again I see this confusion. The Universe is NOT, was NOT, and NEVER CAN BE, a black hole. Why ? I hear you scream. Because a black hole has an asymptotically flat spacetime around it, and the Universe has nothing around it (in fact, not even nothing). A black hole is only defined in terms of the spacetime around it, whilst the Universe is defined purely internally. The reason for the apparent coincidence that the mass of the Universe at which it is just closed and the apparent radius of the Universe obey the same relation as the mass and radius of a black hole, is that they are both governed by Einstein's equations. In fact, if you're still not convinced, look at it this way: if the Universe is just closed, then it's gravitational energy balances it's kinetic energy of expansion. Thus, the net energy of the Universe is zero - and since it's the total mass-energy which enters into the black hole formula, it's clearly wrong. -- Nigel Sharp [noao!sharp National Optical Astronomy Observatories]
sharp@noao.UUCP (Nigel Sharp) (12/11/84)
How embarrassing ! In my previous article, replace the first two "it's" by "its", and leave the second two "it's" alone. Sigh. -- Nigel Sharp [noao!sharp National Optical Astronomy Observatories]
cjh@petsd.UUCP (Chris Henrich) (12/12/84)
[] > > If the whole universe was ina speck, said spec would have been a black hole > > and the "big bang" could not happen. No one has yet disputed this. Why not? > perhaps it reached critical mass and exploded? :-) :-) So the universe was inside a black hole, and nothing could :-) escape... as far as I can see, nothing *has* escaped; :-) everything is still inside the same black hole. It's just a :-) bit roomier now... When cosmologists say that "in the beginning" the universe was in a speck, they mean to say not only that all matter was concentrated into a tiny volume, but also that this volume contained all there was of space. Today the radius of the universe, if it is finite and well-defined, is billlyuns and billlyuns of light years; for many purposes, "infinity" (and the universe is flat). Here is an analogy that is not too bad: imagine a rubber baloon, painted black with white spots. Let the baloon inflate; then the white spots move apart from each other. Initially, when the baloon is very small, the spots are close together; if the baloon was the size of a "speck", then all the spots were crammed together in a speck. This expanding, spherical universe is quite different from the Schwarzschild solution of the Einstein equations which is commonly known as a "black hole." One difference is that the black hole is a stationary or slowly changing configuration, whereas the expanding universe clearly is rapidly changing. Regards, Chris -- Full-Name: Christopher J. Henrich UUCP: ..!(cornell | ariel | ukc | houxz)!vax135!petsd!cjh US Mail: MS 313; Perkin-Elmer; 106 Apple St; Tinton Falls, NJ 07724 Phone: (201) 870-5853
greenber@acf4.UUCP (12/12/84)
<> "Alvie, why are you so depressed?" "The Universe is expanding...one day it will collapse" "Brooklyn is NOT expanding...Now do your homework!"
wkp@lanl.ARPA (12/13/84)
>>> If the whole universe was in a speck, said spec would have been a black hole >>> and the "big bang" could not happen. No one has yet disputed this. Why not? >> [me:] >> The answer is that the matter in your speck never crossed the "event >> horizon" of the universe, i.e., it never escaped from the black hole........ > [Sharp replies:] > Oh dear me no ! Over and over again I see this confusion. The Universe is > NOT, was NOT, and NEVER CAN BE, a black hole. Why ? I hear you scream. > Because a black hole has an asymptotically flat spacetime around it, and the > Universe has nothing around it (in fact, not even nothing). > A black hole is only defined in terms of the spacetime around it, whilst the > Universe is defined purely internally. The reason for the apparent > coincidence that the mass of the Universe at which it is just closed > and the apparent radius of the Universe obey the same relation as the mass > and radius of a black hole, is that they are both governed by Einstein's > equations. In fact, if you're still not convinced, look at it this way: > if the Universe is just closed, then it's gravitational energy balances > it's kinetic energy of expansion. Thus, the net energy of the Universe > is zero - and since it's the total mass-energy which enters into the > black hole formula, it's clearly wrong. > -- > Nigel Sharp [noao!sharp National Optical Astronomy Observatories] [I reply in utter frustration:] Bogus, bogus, bogus, bogus, bogus! Off the scale on the bogus meter! Come on, Nigel, I'm sure they didn't teach you to obfuscate the issues like that in Her Majesty's schools. Let me remind you of the original question: how could mass be blown off the extremely massive speck which contained all the mass in the universe. This is a classical problem, and can be solved without any recourse to Einsten's equations. This may be a sore point with those who prefer to define black holes in a purely formal way, i.e., by defining them as certain highly-specialized exact solutions of Einstein's equations [e.g., see McVittie's article in the British journal _The Observatory_ vol. 98, p. 272 (1978).] If all you're saying is that a big-bang universe is not described by a solution to Einstein's equation because the asymptotic space-time boundary condition is undefined, you are correct. However, let's answer the question, shall we? As Laplace himself solved this problem [see Hawking & Ellis's book on the large scale structure of space-time] I am quite confident of the solution, and I trust you are too. In any case, if all the mass of the universe was centered in a speck, the absolute limiting distance that a particle with velocity c can traverse is R=2GM/(c**2). As long as it is within this distance, no physical laws are violated, which accounts for the fact that this is * n o t * an inconsistency in the Big Bang theory. bill peter los alamos
wls@astrovax.UUCP (William L. Sebok) (12/14/84)
> This expanding, spherical universe is quite different > from the Schwarzschild solution of the Einstein equations > which is commonly known as a "black hole." One difference is > that the black hole is a stationary or slowly changing > configuration, whereas the expanding universe clearly is > rapidly changing. No. In the black hole solutions it is a bit tricky what is meant by time and space, especially since inside the horizon the roles and space are reversed. In the reference frame of one falling into a black hole the black hole is a quite dynamic collapsing universe. Time reversed black hole solutions exist, sometimes called "white holes". The main problem with such a solution is that it is not known how one could exist except if it existed from the beginning. However this is not a problem if the white hole is our whole universe. -- Bill Sebok Princeton University, Astrophysics {allegra,akgua,burl,cbosgd,decvax,ihnp4,noao,princeton,vax135}!astrovax!wls