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Author  Topic: Black Hole Universe Model Questions  
Census Takers Hatmaker Junior Member (Idle past 2871 days) Posts: 4 Joined:

1) THE HUBBLE CONSTANT
Averaging the values measured for the Hubble Constant by i) the 2010 Hubble Space Telescope (gravitational lensing) gives a value for the Hubble constant of 71.35 +/ 2.5 km/s per megaparsec. Put simply at a distance of 3.26 million light years apart, galaxies will recede from each other at a velocity of 71.35 kilometers a second. The Hubble law states that the greater the distance between galaxies the faster they recede from each other so... Scale this up until you get a recession velocity of the speed of light in a vacuum (299,792,458 kilometers a second) and the galaxies would be about 13.7 billion light years apart. Anything further away from you than that... well, it's moving away from you faster than the speed of light and you'll never see it. In other words what we've been calling 'our universe' all this time is just the little chunk of our universe that we can see. It's supposedly entirely conicidental that the universe is reckoned to be about 13.7 billion years old... anyway, it's a hell of talking point... 2) BLACK HOLES AND SUCH It's important to distinguish between singularities and event horizons when discussing black holes. It's also important to distinguish between astonomical and cosmological scale black holes as the energy levels associated with them differ vastly. Bearing in mind that our universe began in a singularity (all that mass in that tiny space) and that if a black hole were the same size as our universe is now, it would have about the same mass, temperature, behave pretty much the same way etc... Think of the edge of our universe today as being the event horizon of the black hole. In very early times the disrtance between the singularity and the event horizon would have been incredibly small. As the universe expanded the distance between the singularity and the event horizon increased, and during the inflationary epoch the horizon (and everything else in the universe) would have been moving away from the singularity faster than the speed of light. The really great thing about black holes billions of years wide is that you could fall freely through one your whole life and never hit the singlularity. And as for falling into a singularity that's already moved away from you in excess of lightspeed... ok, I'll stop now.


Census Takers Hatmaker Junior Member (Idle past 2871 days) Posts: 4 Joined:

Hi Catholic Scientist. Thanks for the welcome. I'll do my best to answer those questions, but Son Goku's already done a beautiful job of explaining the relationship between a black hole's size, mass and density, so I'll just fill in as many blanks as I can.
I'm going to try never to use more than minimal mathematics and jargon on here, as A) I'm a firm believer in the idea that if a concept can be explained fairly simply first without resorting to them, the mathematics that follows is simpler to contend with. B) I don't have a lot of free time, and there are people like Son Goku here who are way quicker and better at explaining that sort of thing than me anyway! C) I'm out of practice and making music occupies most of my time these days (see B).
Think of the Census Taker as being that theoretical immortal observer who witnesses everything, and the "hat" as being the only place they could possibly live to make such observations  a zero cosmological constant (supersymmetric) universe where if you wait long enough you can observe anything that happens in the rest of the multiverse... or possibly killed by gravity waves... anyway, it's a low grade cosmological pun, which is exactly the sort of thing that keeps me off the streets.
I think the best thing I can do here is recommend Leonard Susskind's lectures on Black Holes and Holography. Lecture one alone covers much of interest, starting from the first ideas of 'dark stars' through to black hole complimentarity, which explains how an observer outside a black hole sees something entirely different to an observer inside one. He's especially interested in cosmological sized black holes. The lectures may be a little lores and the sound may be crummy at times but Susskind is a fine lecturer (he's also the guy that coined the "Census Taker's Hat" phrase) and I'd recommend lecture 1 to anyone wanting to get to grips with black holes.
As long as the black hole exists there will be a singularity at the heart if it and its boundary will be the event horizon. The best description of a singularity I can offer is a single point where the curvature of spacetime becomes infinite and where all of the mass of the black hole is contained. For a rotating black hole this point would become smeared out into a ring. The point being that the singularity does not extend all the way to the event horizon. The horizon is simply the point of no return. Once you cross the horizon you've got a hot date with a singularity sooner or later, but the larger the black hole the longer it'll be before you hit it. There is also the argument that what we refer to as a gravitational singularity is just the point at which general relativity fails. But that's one for the string theorists.
If our universe is a black hole, we would not be past the event horizon, as we are inside the black hole. We'd be behind the horizon. As to exactly where the singularity is these days, I'd throw that open to better minds than mine to answer... ...but I'll put my neck on the block and suggest it may not be in the little 13.7 billion light year radius patch of our universe that we'll never be able to see beyond... and if during the inflationary period everthing moved away from everything else at velocities many times in excess of light speed, it's possible the singularity may be out of causal contact with the rest of the universe. Naked cosmological singularites? I just don't know. Over to better minds than mine. Edited by Census Takers Hatmaker, : Typos, not sure I got them all but spellcheck is sooooo last season


Census Takers Hatmaker Junior Member (Idle past 2871 days) Posts: 4 Joined: 
Hi Dr. Adequate. I know it's a bit presumptuous to respond to a question aimed at someone else with the best part of a thousand words, but this might be of assistance to anyone wanting to get a handle on big crunch/big rip scenarios...
USEFUL INFORMATION ABOUT YOUR UNIVERSE The fate of the universe (big crunch, big rip etc.) depends on a few key factors and is best described by three simple universe models. To the best of our knowledge, about 73% of the energy in the universe is contained in the vacuum of empty space. This is often referred to as 'dark energy' and sooner or later you're bound to meet someone at a party with an adenoidal voice who'll talk about it at great length and tell you "they call it that because nobody knows anything about it..." This may be of some use to fend off such people: A) THE COSMOLOGICAL CONSTANT: The higher the energy density of the vacuum energy, the faster the universe will expand. If it's too high it will expand so quickly that structure will not be able to form. This is known as a 'big rip'. If the energy density is too low, the universe won't be able to expand enough to overcome gravity and it will collapse. This is the 'big crunch' scenario. So far so good. Now for the tricky bit... the vacuum energy density is known as the cosmological constant and it can have a positive, zero or negative value. The value of the cosmological constant in your universe will be the absolute minimum energy density anything in your universe can ever have. The reason for this is that empty space isn't empty. The vacuum is made of particle/antiparticle pairs that constantly blink into existence and rapidly annihilate each other. These are called 'virtual particles' by some and 'quantum fluctuations' by more helpful people... but more on quantum fluctuations in a minute. B) FERMIONS AND BOSONS: Don't forget everything anyone ever told you about particles, but take comfort from the fact that they only come in two basic varieties.  FERMIONS are the particles that emit and absorb energy in the form of BOSONS, which once emitted travel freely until they meet another fermion.  FERMIONS consist of quarks (up, down, strange, charm, top and bottom), and leptons (electrons and neutrinos, muon electrons/neutrinos, tau electrons/neutrinos)  BOSONS (or more correctly the gauge bosons) come in different varieties for different fundamental forces  Photons (electromagnetism), Gluons (strong nuclear force), W+, W and Z bosons (weak nuclear force). There are also meant to be Gravitons (gravitational force) but they're going to be extremely hard to detect and Higgs Bosons which should hopefully be a done deal by the end of the year. C) THE BASIC COSMOLOGICAL MODELS  1) EXPANDING UNIVERSE  POSITIVE COSMOLOGICAL CONSTANT If a universe has a high enough cosmological constant to overcome gravity, it will continue to expand. The further away from each other objects in such a universe are, the faster they will recede from each other. Such a universe would have negative spatial curvature, like the surface of a saddle. If you drew a triangle on such a surface, the lines would not be straight but would curve inwards like the surface of a concave lens. The interior angles of such a triangle would add up to less than 180 degrees. An expanding universe with negative spatial curvature would have a positive cosmological constant, and it would be dominated by bosons.  2) SUPERSYMMETRIC UNIVERSE  ZERO COSMOLOGICAL CONSTANT This is the weird one. A universe with no cosmological constant has no vacuum energy. It would expand, but the rate of expansion would decrease as time went on. In other words, it wouldn't grind to a total halt but after a while you'd be hard pressed to tell. Such a universe would have no spatial curvature. There would be no quantum fluctuations as there is no vacuum energy. Neither bosons or fermions would dominate, their contributions would balance equally.  3) CONTRACTING UNIVERSE  NEGATIVE COSMOLOGICAL CONSTANT Now we come to the case of positive spatial curvature  indicating a closed and bounded universe. Picture a triangle drawn on the surface of a sphere. The sides of the triangle would be curved lines instead of straight ones. The interior angles of this triangle would add up to more than 180 degrees. The cosmological constant in a universe of this kind would have a negative value. This would mean that the further objects were away from each other, the greater an attraction they would exert on one another. A universe like this would end in a big crunch scenario, and would be dominated by fermions. D) CONCLUSIONS? Well, maybe not conclusions but if you've read all that, then it might interest you to know:  Our universe has a small positive cosmological constant  Our universe is dominated by bosons  just taking photons alone... if you added up the total of all the other particles in our universe and took that total, it would still only come to roughly a billionth of the amount of photons there are. Although a very small negative spatial curvature has been measured for our universe (by taking very large scale measurements of it) the result was not concise enough. The margin of error is significant enough that it’s not possible to dismiss a positive curvature scenario... but it's not looking likely.  To the best of my knowledge (how's that for a disclaimer?) the only viable models that have been constructed for cosmologies with a negative cosmological constant are antimatter dominated universes.



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