rrm (11/15/82)
Why don't we get into a discussion on black holes. I am interested in this topic, but I must admit I have very little knowledge of the subject. I believe a quite interesting and entertaining discussion could be carried on over this net. Also, I have a specific question for anyone on the net who may be knowledgeable about black hole theories. I have seen reference on the "horizon" of a black hole. What is this exactly and how (if it is related) does this effect the Schwartzchild radius????? If anyone replies to this, please post it on the net instead of sending me mail. Then the rest of the world can benefit from the theory. Ron Meyer inuxa!rrm Bell labs - Indy
kek (11/16/82)
In response to inuxa!rrm (Ron Meyer) question on black holes:
The German astronomer Karl Schwarzschild determined the field equations
describing space-time in the vicinity of a spherical lump of matter. His
solution states that if the mass is compressed within a certain radius
(called the Schwarzschild radius) space-time is so severely distorted
that nothing, even light, is able to escape. To put it another way,
the "local gravity" cannot be overcome. The Schwarzschild radius (R)
for a body of mass M is:
R = 2GM/c**2
where G is a constant of proportionality known as the universal
gravitational constant, and c is the velocity of light. Thus the
Schwarzschild equations define how compressed a body would have to
become to create a black hole. (Actually, Michell and Laplace hinted
at such a possibility nearly a century before Schwarzschild put it
all together).
A body thus compressed (e.g., a collapsing star) disappears from view
since light is unable to escape from its surface (it has become a
black hole). The boundary of the black hole is called the "event
horizon" because nothing inside can ever pass to the outside. The
event horizon is a one-way boundary: you can check in but never out!
This boundary coincides with the Schwarzschild radius. Even if the mass
inside continues to collapse into a "singularity", the event horizon
remains the same, the Schwarzschild radius. This holds true for
simple non-rotating black holes. Rotation adds some complexity.
As a couple examples, the Schwarzschild radius for our sun is just
under 3 kilometers (it's nominal radius is about 700,000 km) and
for the Earth is a little less than one centimeter!
Three good references on the subject that I have read are:
GRAVITY, BLACK HOLES AND THE UNIVERSE
Iain Nicolson
John Wiley & Sons - New York 1981
MONSTERS IN THE SKY
Paolo Maffei
The MIT Press - Cambridge, Mass and London, Eng (1980)
BLACK HOLES - THE EDGE OF SPACE, THE END OF TIME
Walter Sullivan
Anchor Press / Doubleday - Garden City, NY (1979)
Ken Kepple
Bellabs - Holmdel
5941ux!kekleichter (11/16/82)
The horizon (more fully, event horizon) of a black hole is the surface in space at which the escape velocity is the speed of light. (This is an informal way of putting it but is probably correct if interpreted right.) If you are outside the horizon, you can get away from the black hole. Inside, you can never escape. Hence, no information can ever cross from inside the event horizon to outside of it. (If you are exactly at the event horizon, under the right conditions, you can orbit forever, but never get away.) In the relatistic view of things, two events can be causally related only if infor- mation could have propagated from one to the other at no more than lightspeed. No event whose spacial location is inside the horizon can be the cause of an event outside of it. A better - certainly more accurate - way of looking at it is as follows: General Relativity views gravity as consisting of a curve in 4-dimensional space time. The effect is to rotate the reference 4-d coordinate system. As you move closer to a large mass, the rotation is such as to rotate the time axis somewhat toward the mass. On result is the slowing of time in a large gravitational field. The field of a black hole is so large that once you cross the event horizon the direction of the time axis is toward the black hole! Hec \\\Hence, to escape you'd have to have a time machine! I believe that the Schwartzchild radius and the event horizon coincide, at least for a non-rotating black hole. It's been a while since I looked at this stuff; I apologize for any errors - which I'm sure someone in net-land will point out. -- Jerry decvax!yale-comix!leichter leichter@yale
whaley (11/17/82)
#R:yale-com:-33700:uiucdcs:24400020:000:219 uiucdcs!whaley Nov 17 10:57:00 1982 Last year I heard a lecture here that claimed that it is now believed that particles can tunnel out of the event horizon, and preliminary calculations about the amount of energy show that it may extremely significant.
DCP@MIT-MC@sri-unix (11/19/82)
From: David C. Plummer <DCP at MIT-MC> Now wait a minute... if information inside the event horizon is only allowed to travel toward the center, how does the information that the gravitating body is rotating travel outward to affect some aspects of the black hole?
knutsen@SRI-UNIX@sri-unix (11/19/82)
From: Andrew Knutsen <knutsen at SRI-UNIX> Also, if we accept the gravitational-wave hypothesis, a lot of information about the internal dynamics of the object could radiate away. Each black-hole-quake could be detected. Perhaps this sort of thing is why gravitational waves are so controversial...
leichter (11/20/82)
The radiation seen "coming out" of a black hole, in Hawkings' theory, is carefully worked out. It turns out that a black hole is also "black" in the thermodynamic "black body" sense; it is a radiator with an equivalent temperature. The temperature turns out to be proportional to 1/A, where A is the area of the black hole; "area of what" needs careful definition. (It's of the sphere at the Schartzchild radius for a non-spinning black hole, I'm pretty sure.) Now, a black body is a RANDOM radiator; any combination of particles with a given energy is as likely to be radiated as any other. Hence, given enough energy, a TV set COULD come out - although it's very, very unlikely! The radiation caries away energy, hence masss; so the black hole gets lighter. The area shrinks, all other things being equal, as the mass goes down. But this means the temperature goes up, implying more radiation. So the actual radiation pattern you see is a gradual but accerlerating increase; the black hole eventually vanishes in a burst of gamma rays. (In fact, if there were small black holes created in the big bang, we should see gamma ray bursts from their collapse. We don't. This implies that there could not have been to many black holes of such a size that we'd see them exploding now.) Note that when a black hole explodes in this way, NOTHING is left - you do NOT get the original object back. It's wrong to try to extend your normal view of the world "into" a black hole. A black hole is TOTALLY specified by just three quantities: mass, charge, and angular momentum. It is im- possible to determine anything about what went into the black hole other than that the total of such things gave those three numbers. It turns out that, if you take a black hole with a given mass, charge, and AM, and calculate the set of all particle configurations that could have collapsed to give that black hole; and consider that you have lost the in- formation that specified which of those configurations you started with; and hence have increased entropy by that amount; you can calculate an equivalent temperature, thermodynamically, for the black hole. You guessed it - the result is the same as for the calculation done the other way (calculating the probabilities of all virtual particle pairs that could form near the black hole and have one of the pair disappear into the hole while the other radiates). I should note that the equivalent temperature of a black hole of any reasonable mass is tiny. If I remember right, a black hole with the mass of the sun would have an equivalent temperature of 10**-4 degrees absolute. Finally, one point that is often missed is the distinction between black holes and singularities. The General Relativity field equations place some constraints - which are very tough to evaluate in detail - on what the space- time "fabric" can look like. They allow for singularities - places where the usual metric structure breaks down. A singularity is not a black hole - rather, it is a region of space-time of a particular form that SURROUNDS a singularity. Such a singularity is "nice" because it is shielded from view by the black hole - we can never observe the really crazy things that can go on in the region of a singularity - physical laws just break down. A "naked singularity" - one we could actually observe - would lead to all sorts of problems for our world-view; causality breaks down, for example. Hence, most physicists believe that the field equations do not allow a naked singularity. However, the last I heard, no one had proved this. (I think it is known that the only spherically symmetrical singularities are inside of black holes.) -- Jerry decvax!yale-comix!leichter leichter@yale
tzs@mit-ccc@sri-unix (11/23/82)
Lot of the questions out there happen to be cofcerning the thermodynamics
of black holes. Well, Kip Thorne wrote a very good article for Sci Am
which ended up in the "Cosmology +1" collection. Pretty much, there are
only three quantities of a mass that can be conserved after it falls into
a black hole--better yet, say that are conserved--the mass of the object, the charge, and the angular momentum. (This was all summed up in the statement "Black
holes have no hair." It turns out that black holes do decay over time. You can
think of this as a virtual particle-antiparticle pair being created right
near the boundary of the black hole--one of the two gets snarfed in, and the
other is free to go whither it will. To an outsider, this looks like a particle
is being emitted from the black hole. The rate of decay varies inversely with
the mass of the black hole. I seem to remember that your average ordinary
black hole was supposed to not be at absolute zero, but at app. 0.0001 degrees
Kelvin. It also turns out that the baby black holes that were supposedly
created in the Big Bang are supposedly reaching the end of their decay and if
such a decay were seen, it would liberate approximately the energy in a
supernova.) I'll check my numbers---it's been a few years since I read it.
--tzs---goodale@fortune.UUCP (Dave Goodale) (05/15/84)
Subject: black holes
Newsgroups: net.physics net.astro
NEW INFORMATION ON BLACK HOLES
Noted Authority Clears Up Confusion
It has come to the attention of this office that much complete
balderdash has been promulgated recently regarding the class of
astronomical objects usually referred to as "black holes". One expert
makes one paradoxical claim, another makes another ... usually in
tones of infuriating condescension ... the time has come to cut
through this Gordion knot and see if with LOGIC we can make some sense
out of the nonsensical gobbledegook that these math priests throw out
in such confusion profusion.
1) CONCLUSION ONE: If we could somehow get hold of black hole,
only a small one ( a couple of miles across ) and drop it on Russia -
we could make a fortune.
2) With Russia on her knees, we would also have an immediate
solution to the garbage crisis ... also housing, jails, etc.
3) Publicity is a problem ... people don't relate all that well
to black holes. Black holes have an image problem. People perceive them
as somehow ... dark ... threatening ... Let's face it, the very name
"black hole" is a turn-off. Black holes need some good PR work to
offset their "bad rap". For instance, its not true that stuff that is
dropped into a black hole vanishes forever. Eventually, the physics
wizards now tell us, the stuff comes back out - maybe a little bit
rearranged. This is a big selling point for people who want to "get
away from it all", or for people who want to put their savings into a
place that is absolutely safe.
4) "Punk" rock is an angle that should be explored here. These
youngsters are naturals for black holes! Bands could vie with each
other to have black holes at their concerts and "social doings", etc.
5) Religion! Need we say more? Meet your maker through the back
door of the universe - down the garbage chute and into the arms of
the almighty!
6) It cannot be denied, from an imagistic point of view, that
the "black hole" brings up certain anatomical comparisons ... even
the name is kind of suggestive - proctologists are naturals for this
approach.
7) Now there are those pundits who state that theory at least
indicates that it would be possible to use a black hole to travel
backward in time and shoot one's grandfather ... in direct
contradiction of the "rational" view of cause and effect ... other
pundits have argued against shooting one's grandfather if the old chap
is at least pleasant, offers one a drink of scotch, etc ... instead
they recommend crushing a bug or perhaps displacing a single electron-
the changes from this would "snowball" until in the present time we
would all be 20-foot pink flamingoes. Now these individuals might
look differently on the matter of shooting one's grandfather. They
might not even have grandfathers ... they might reproduce from viral
infection of bladderworts. What then, pundits? How to shoot one's
grandfather then?
8) There is one final matter - one last question relating to
black holes that seems to stump everyone. That question is ...
"other universes". Supposedly the black hole is the gateway ( if you
don't mind being torn to pieces, irradiated with super-hot gamma
rays, and then crushed down to absolutely nothing ) to "other
universes". Now on this subject of "other universes" no one seems to
have one God Damn sensible thing to say. Sometimes the gurus hint
that the other universe is "similar to our own" - but there is a
timid tone to their assertions that betrays that the speaker wonders
if he dropped a sign somewhere and anyway can't understand his own
equations. Sometimes they say that the black hole just pops out again
in our own universe. Sometimes they say that our own universe itself
popped out of a "white hole" type singularity and that previous to
this there was "no time", "no space", "no causality" and other such
gabble.
The time has come to clear up this whole matter. All this time-
wasting confusion has got to stop, so we can get back to some
PRODUCTIVITY. Let's use some MIND POWER to see if we can blow away
the chaff of fear and superstition and knock some holes in the wall
of non-thought that surrounds this whole concept of "another
universe".
Now here's the key to the whole thing ... if we can get there
through a black hole, its not another universe ... its really part
of our own universe. Right? So ... no problem. We can forget all
about any "other universe". Its all just one big happy universe.
Of course the new place may take some getting used to. Once
we've made the trip, and spruced up a bit, and had a nip of
something strong to counteract the effects of being crushed,
burnt, etc, there may be some "culture shock". It might be
unsettling at first to find that left is always peaches, and that
"reality" is 20-year old hydrogenated crankcase oil ( in short
supply ).
But these are all problems that can be overcome. And now that
the word is out, this office is confident that many farsighted and
right-thinking people will see fit to "take the big step" down
a black hole. Remember, this office will stand behind you - way
behind!elt@astrovax.UUCP (Ed Turner) (06/04/84)
Somehow I thought the Reissner-Nordstrom metric was for J > 0 holes. Of course, it applies to J=0 Q<M holes. Ed Turner astrovax!elt