Conference noted::sf

    re max T.E.:
    
    > >    The minimal condition for forming a black hole is a body dense enough
    > >    to have a surface escape velocity faster than the speed of light.

    >	Ah, but that is the kicker.  If you look at Einstein's general
    > relativity, such densities do very strange things to space and time before
    > the singularity can form. 

      I don't understand how this is so, since it is General Relativity
    that predicts the existance of black holes.
    
                                                   
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    The descriptions of singularities and event horizons given in 362.212
    are correct, but the two are not the same thing.  Both, however,
    are major parts of a black hole.
    
    As you approach any gravitating body, the escape velocity (the velocity
    needed to get away and never fall back) increases.  A black hole's
    event horizon is the point where the escape velocity is equal to
    the speed of light.  Hence (barring FTL weirdness) nothing crossing
    the event horizon can ever get back out again.  The event horizon
    is the spherical "skin" of the black hole.
    
    The singularity, on the other hand, is its center.  It is at this
    place where, according to the equations of general relativity, all
    the mass collapses to a geometrical point of infinite density. 
    
    You can have event horizons without singularities and maybe vice versa.
    We are all inside a vast spherical event horizon with a radius of
    about 15,000,000,000 light years.  This is the point beyond which
    no light can reach us, because not enough time has yet elapsed since
    the Big Bang.  This particular event horizon is, of course, expanding
    all the time and, like an everyday horizon, has a different position
    depending on where in the cosmos you are standing.
    
    Some people worry about the existence of "naked singularities" without
    event horizons to shield them from our chaste eyes.  You see, it
    is possible to extract energy from a black hole by various means.
    Using some methods, you can reduce the mass of the hole to zero.
    There is then no mass to create the event horizon.  Does the
    singularity that theoretically lurks at the bottom also go away,
    or does it stay there, doing God knows what?  Last I heard, no one
    knew.  (Naked singularities could be amusing, metaphysically, but
    the presence of singularities in the theory might just indicate
    the limitations of the theory, not the presence of real singularities
    in nature.)
    
    If the black hole rotates (almost all of them would), you get
    wormholes, with a black hole at one end and a white hole at the
    other.  As you approach the singularity, the curvature of space
    becomes greater and greater.  If the hole rotates, there are possible
    paths that take you to regions of smaller and smaller curvature,
    until you are out in essentially flat space again.
    
    About time and black holes: The time distortion DOES mean that,
    for a distant observer, it takes forever for an object to fall all
    the way into the hole.  However, it very quickly gets snuggled up
    to the horizon.  From the object's point of view, it falls through
    the even horizon and into the singularity very quickly.  Even if
    there is no singularity, there will be serious tidal forces inside
    to worry about.
    
    Earl Wajenberg

    re .2:
    
    Super explanation! 
    
    But of course I do have a question, except this time it really is
    a question and not an objection.
    
    > If the black hole rotates (almost all of them would), you get
    > wormholes, with a black hole at one end and a white hole at the
    > other.  As you approach the singularity, the curvature of space
    > becomes greater and greater.  If the hole rotates, there are possible
    > paths that take you to regions of smaller and smaller curvature,
    > until you are out in essentially flat space again.
    
      Could you expand on this some? This is the real meat of the issue
    of black holes.
                                                   
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    Thank you.
    
    I'm not really competent to expand on it much further.  I'll try
    to remember to bring in what literature I have on general relativity.
    
    Earl Wajenberg

    Another question.
    
    What is the mathematical/quantum physics status of this theory ?
    and what are the implication (apart from the fact that if black
    holes exist then you could travel FTL to other points.
       Would attaining C create a black hole in your vicinity, there
    by allowing a jump into hyperspace and out again ? I'm just trying
    to piece together my limited knowledge.
    
    Winton

    I recall a theory for extracting energy from black holes by 'tossing'
    matter (waste in this case) into them.  Matter, when dropping into
    the gravitational pull of a black hole, emits radiation.  I dont
    remember the reason behind this, but perhaps it has something to
    do with the stress of the tidal forces on matter.  Could someone
    provide me with an explanation of this phenomenon? 
    
    Dan

    Re .6:
    
    I think that is actually a simple phenomenon.  You don't even need a
    black hole for it; we do it on Earth.  We find a nice place where there
    is water coming by and arrange for it to fall toward the Earth, turning
    a generator in the process.
    
    With black holes, you just get fancier.  Drop an electron into it, the
    electron accelerates, accelerating charges emit radiation, voila, you
    have energy.
    
    
    				-- edp 

    re .5:
    
    > What is the mathematical/quantum physics status of this theory ?
    
    If you mean the general theory of relativity, the status is that
    Stephen Hawking is working on combining it with quantum mechanics.
    Some very interesting things are coming out of his work. I refer
    you to his paper "The Edge of Spacetime" in _American_Scientist_
    Vol. 72, July-August 1984, pp 355-359.
    
    > and what are the implication (apart from the fact that if black
    > holes exist then you could travel FTL to other points.
    
    One implication is that black holes are not forever, they do radiate
    energy and therefore mass and over time simply evaporate.
    
    > Would attaining C create a black hole in your vicinity, there
    > by allowing a jump into hyperspace and out again ? 
    
    I don't think so, the thing is "your vicinity" becomes a very
    poorly defined concept near light-speed. As I understand it, as
    you approach light-speed you tend to get stretched-out"  perpendicular
    to your direction of travel. the limit at light speed is to be smeared
    over all space-time, which is why you "can't get there from here".
    This "smearing" is what prevents your infinite mass from generating
    a black hole.
                                                   
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    I dimly recall a description of getting emergy out of black holes
    by using them as garbage dumps.  Put fancifully, you send a garbage
    can on a tight orbit around the hole.  Somewhere near closest approach,
    the can ejects the garbage.  The garbage falls into the hole.  For
    mysterious relativistic reasons that I don't recall, the can acquires
    kinetic energy in excess of the mass energy of the garbage.  This
    energy gain decreases the net energy of the black hole.
    
    You don't get extended along your line of flight; you get contracted.
    The effect is even called Lorentz-FitzGerald Contraction.  As a
    body approaches the speed of light, its length along the line of
    flight approaches zero; it tries to become two-dimensional.
    
    Both quantum mechanics and general relativity have so far survived
    every experimental test of their accuracy.  Some of these tests
    have gotten very, very finicky, too.  It is therefore awkward that
    combining the two theories seems next to impossible, so it is a
    good thing that we have a genius like Hawking working on it.
    
    Earl Wajenberg

    re .9:
    
    The extension does not occur along the direction of flight but
    perpendicular to it. But thanks for pointing that out.
    
    A two dimensional, infinite sheet of material will generate a uniform
    field thoughout all space and thus not be detectable. It would just
    be a DC bias so-to-speak (can you tell I'm a EE?)
    
    The "garbage-can" effect may be a result of quantum, not relativity?
    Also, might it not be a simple newtonian effect of jettisoning the
    mass that will throw you into a higher orbit?
    
                                                   
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    Re .10:
    
    There is no extension in any direction, only contraction in the
    direction of travel.  You cannot attain lightspeed because you would
    have to have an infinite source of energy to do so.
    
    
    Re .9:
    
    > Both quantum mechanics and general relativity have so far survived
    > every experimental test of their accuracy.
    
    I believe general relativity has failed many tests in the realm where
    quantum mechanics works best and vice-versa.
    
    
    				-- edp 

    Re .11
    
    I have not heard of any failures for either theory.  I would be
    interested to hear more.  Do you recall where you heard this?
    
    Earl Wajenberg

    Re .12:
    
    I heard it from a teacher, although I think I've seen it in various
    places.  It is well known; why would physicists be worrying about
    unifying General Relativity and Quantum Mechanics if each correctly
    described all experiments?  They would already be combined.
    
    
    				-- edp 

    	Do you realize that if black holes (how about calling them
    collapsars) are gateways to other universes - and if our descendants
    decide to use them as garbage dumps - that other universes will
    be getting OUR trash!
    
    	And they might just be doing some collapsar garbage-dumping
    of their own!
    
    	Larry
    

    re .12:
    
    One failure for GTR is the presence of singularities. A singularity
    would provide exact knowledge of both the position and momentum
    of all the particles within. This is how Black Holes evaporate.
                                                   
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    re .14:
    
    Maybe that is what quasars are.
                                                   
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Re: .11
    
    >There is no extension in any direction, only contraction in the
    >direction of travel.  You cannot attain lightspeed because you would
    >have to have an infinite source of energy to do so.
    
    So you would tend to become a pancake of incredibly high density
    getting denser as you accelerate.  What happens when the density gets
    high enough to distort space-time?
    
Re: .10
    
    Couldn't you detect the presence of an infinite plane of matter when
    you hit it?  Or if you passed through it, wouldn't you experience a
    reversal of field polarity?  Even if you calibrate to zero on one side
    the detectors would register a change at the boundary.
    
Re: the topic in general
    
    What would an observer experience as he or she fell into a black hole?
    It seems clear that an outside observer O would see the falling
    observer F moving more and more slowly as F approached the event
    horizon of a black hole.  O would observe F's clock slowing down in a
    corresponding fashion.  O never sees F reach the event horizon.  But
    what about F?  I think F would come up to the event horizon and pass it
    moving at a healthy (or unhealthy) clip.  At that point, its anyone's
    guess.  We can't even say for sure whether gravity continues to
    increase.  Neither do we know of the distribution of mass beyond the
    event horizon.  If one assumes that gravititational acceleration
    continues to increase, then I think singularity is a good bet barring
    any effects from as yet unknown forces. 
    
    It seems there could, however, still be factors preventing F from
    actually reaching the event horizon.  For example, what is the
    curvature of the space-time continuum there?  Is space-time so
    distorted there that F still measures vast distances being traveled at
    enormous speeds?  Does F see the event horizon receding at he
    "approaches" it?  As a final question, what would the rest of the
    universe look like to F? 
    
	Thanks,

	 /~~'\
	W o o k
	(  ^  )
	 \`-'/
	  \_/

    Re .17:
    
    Any mass is enough to distort space-time.
    
    
    Re ?:
    
    This wasn't in this note, but I can't find the response I want, so I'll
    mention it briefly:  It may well be that timelike distances permit
    causality.  On reflection, I would think that the names would be
    selected so that a purely time separation is timelike -- I'd hate to
    think time weren't timelike, and a pure time separation obviously
    permits causality, while a pure space separation does not. 
    
    
    Re .*:
    
    I recall seeing a book which discussed the solutions which had been
    found for the field equations.  Unfortunately, I don't remember
    the title.
    
    It seems a black hole only has three or four properties.  Three
    are mass, charge, and rotational energy.  I do not remember if there
    was a fourth.  The temperature of a black hole is a function of
    its mass.
    
    These properties give rise to several varieties of black holes.  The
    simplest is a hole with no charge or rotation.  This black hole has one
    event horizon.  Space-time inside the event horizon is fairly normal,
    at least compared to what is to follow.  Crossing the event horizon is
    painful (but could be done in theory?).  It is, like all of crossings I
    recall, a one-way trip.
    
    The fun begins when you add a little charge to the black hole.  Then
    the single event horizon becomes two.  Inside the innermost horizon,
    space-time is again normal.  But between the two horizons, I think time
    and space are somewhat interchanged (from the position of some observer
    with a really good telescope).
    
    If you add enough charge, you can get a naked singularity -- a black
    hole you can cruise up to and sneeze at.  Make sure your ship is
    structurally sound before you get too close.
    
    The last situation I will discuss involves adding rotation.  Then the
    black hole forms a torus (doughnut).  I don't recall if it requires no
    charge or lots of charge to get this situation:  There is a horizon in
    the hole of the torus.  As you increase the rotation, the hole's hole
    gets bigger, and the distortion of space gets less.  You can take your
    flimsy spaceship on a one-way cruise into another universe.  It is
    one-way because the universe you go into won't have any paths back to
    your home universe, but only onward into more universes.  Take lots of
    luggage.                                                     
    
    (This is all recollection from several years ago.  Can anybody confirm
    it?)
    
    
    				-- edp

Re .0:

	I wish you had included some of the other replies in the original 
note to establish the proper context.  One of the points I was trying to make 
was that the singularity was an artifact of the math, not a real phenomenon.

	To restate one of the original arguments - The Schwartzchild solution 
has part of its initial conditions the fact that space is Euclidean embedded 
in it by way of specifying the relation between the radius and the volume 
contained within that radius.  Since general relativity requires that
space/time be curved by the presence of mater, all the curvature required has
to be accounted for by distortions in the relative time rates.  The
Schwartzchild solution gets around this by imposing time invariance.  This in
turn requires that black holes have to have constant mass, neither shrinking
or growing.  In other words, the Schwartzchild solution to Einstein's 
general relativity is a limiting case, not a physically realizable situation.
In reality, there is no singularity.

	One of the situations that approaches the limit is the colapstar.  

	Exactly what happens depends on your point of view.  From the point
of view of a distant observer, it is reasonable to assume that the relatively
Euclidean space in the observers vicinity extends into the region of the
colapstar.  If you make this assumption, you have to give up the assumption
that the speed of light is constant (note that this is different from the
assumption that the speed of light APPEARS to be constant) since the relative
time rates (the speed of light relates the geometry of the space with time)
between the observer and objects in the vicinity of the colapstar are so
different.  In this case, the formation of the singularity is postponed 
indefinitely by the distortion.

	If you take a point of view at the center of the colapstar, things
appear to be quite different.  Since interactions are taking place between
the observer and the colapstar, it makes sense to assume that the speed of
light is in fact a constant and that time is relatively invariant.  In this
case, distortions in space account for the space/time curvature.  One of the 
most noticeable results of this distortion is that the volume enclosed within 
a spherical surface is much larger than a sphere with the same surface area 
would contain in a flat space.  In fact, space can become so distorted that 
the change in surface area of a spherical surface can start to increase as 
you approach the center, rather than decreasing as it usually does.  In this 
case, formation of the singularity is defeated by the reduction in density 
caused by the spatial distortion.  I'll come back to this in a minute, but a 
couple points about charge and rotation need to be dealt with first.

	If the colapstar has a net charge, the charge will be stripped from 
the interior of the colapstar and deposited on its surface.  This follows 
from the fact that a colapstar is composed of conductive material (plasma) 
rather than insulating materials.  By their very nature, unpaired electrical 
charges try to get as far away from each other as possible.  Thus the initial 
distribution of charge would be on the surface of the colapstar.  As the star 
collapses, the material in the center of the star gets further and further 
away from the surface, and the forces holding the surface in place become 
less and less while the electrical forces trying to tear the surface apart 
become stronger and stronger.  The result is that the 'black hole' at the 
center of a colapstar can never have a charge in its own right, but it can be
surrounded by a highly charged region.  In a similar manner, any rotation
inherent in the material of a colapstar will be stripped out and left behind
during the collapse.  (Alas, no worm holes either.)

	Now to get back to the fascinating geometry of a colapstar.  As noted, 
a colapstar will be very big inside and will be surrounded by a very small 
surface.  This makes it very difficult to find your way out of a colapstar but 
it is not impossible to do so, given enough resources.  Again, I have run to 
my limit on this.  I will leave it to your collective imaginations as to how 
to continue from here.

			Max TenEyck Woodbury

    re:.16 (quasars = white holes ??)
    
    I've seen it suggested that indeed quasars are white holes.
    
    re: .6 (energy from black holes)
    
    The theory goes that each particle hitting the event horizon breaks
    down into its component particles and anti-particles, each carrying
    energy with it. For each particle that proceeds down the hole, the
    anti-particle shoots off in the opposite direction, away from the
    hole. The energy of the system remains constant, but from our frame
    of reference, energy is being produced by the hole.
    
    --- jerry

Jerry -

	Quasars are the wrong topology for white holes and are much too small.
The biggest problem with quasars is we do not really know how far away they 
are.  Because we do not know their actual distance, we do not know their 
absolute magnitude.  The only estimate that I know of about their distance is
from their red shift.  There are methods for accounting for their recessional
velocity other than the Hubble constant. 

	On black holes and event horizons, assuming such things exist - By
the nature of the event horizon, you can never observe anything hit the event
horizon;  It will seem to take forever for the thing to get there, and even 
longer for any results to get back out.

Re my previous comment:

	My comment about the change in surface area is speculative - I have 
not worked out the mechanism that would generate the stated results in 
enough detail.  The part about the volume is NOT speculation - it falls out 
of the equations directly if you look for the effect and does not require 
either an event horizon or a singularity.

    re .18:
    
    > On reflection, I would think that the names would be
    > selected so that a purely time separation is timelike -- I'd hate to
    > think time weren't timelike, and a pure time separation obviously
    > permits causality, while a pure space separation does not. 
                
      You are in fact correct. "Timelike" is the term for possibly causally
    connected events, whereas events with a spacelike seperation cannot be 
    causally connected.
    
    > It seems a black hole only has three or four properties.  Three
    > are mass, charge, and rotational energy.  I do not remember if there
    > was a fourth.  The temperature of a black hole is a function of
    > its mass.
    
    I've read they have only the three properties you mention.
    as a side note, S.Hawking (whoelse?) wrote a paper called "Fuzzy
    Black Holes Have No Hair" that deals with the effects of these three
    properties on black holes. When I find where it was published, I'll
    post it here.
      
    re .19:
    
    > One of the points I was trying to make was that the singularity 
    > was an artifact of the math, not a real phenomenon.  
      
    I agree that the singularity is an artifact, but not that Black
    Holes are.
    
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   
    After re-reading .19 a few times, I need to have three terms defined:
     
    	1) singularity
    	2) black hole
    	3) colapstar (collapsar)
    
    I do not believe these terms are synonymous. I don't believe that
    they are being used as synonyms but I would like to have the
    definitions explicitely stated.
                                                   
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    	The current most acceptable theory is that quasars are
    early-forming galaxies as seen from billions of light-years away,
    but naturally, since we still know so little about them, almost
    nothing should be ruled out.
    
    	RE 393.18 -
    
    	The word for black holes is collapsar, not colapstar - like
    pulsar, not pulstar.
    
    	Larry
    

(Note: GTR = "General Theory of Relativity"
       STR = "Special Theory of Relativity"
        QM = "Quantum Mechanics"	   )

Re .13

But neither GTR nor QM claims to describe ALL of experience.  GTR, for 
example, says nothing about electromagentism unless you start introducing 
additions like the mutliple dimensions of the Kalusa-Klein (sp?) theories.
QM doesn't say anything about any force unless you start making similar 
additions.

The problem, as I understood it, was that the mathematics blew up in one's 
face in various ways if one tried to combine the theories at the abstract 
level.  At the practical level, as I understood it, the problem was that no 
one has yet found a do-able experiment for which GTR gives one prediction and 
QM gives another.

I *do* know that every now and then I read about a hair-fine test of QM or GTR 
recently made, and the gist of the report is, "Yes, folks, the theory is still 
holding up."

Re .17

What happens when a Lorentz-contracted object gets dense enough to form a 
black hole?  I've often wondered, especially since, from its own reference 
frame, nothing has happened to its density at all.  From its point of view the 
universe has become foreshortened and denser.  Does each see the other fall 
into a black hole?

Re .19

Given their usefulness in explaining quasars and X-ray stars, black holes 
aren't much more "mythical" than neutron stars or quarks.  (These have never 
been directly observed either.)  The singularities at their centers are, I
grant you, more conjectural and a firm belief in their existence shows a 
touching faith that GTR is the Final and Absolute Truth, a commodity science 
does not typically deal in.

Re .22

See .2 on the geography of black holes.  The singularity is the supposed point 
of infinite density and infinite spacetime curvature that lurks at the center 
of a black hole.  I suppose it might exist, but its existence is more 
conjectural than that of a black hole itself.

A black hole is any body with a surface gravitation strong enough to hold in 
light.  That's why it's black.  Such bodies can exist in both Newtonian 
gravitational theory and GTR.  I suppose some future theory might be able to 
exclude them, but at the moment it doesn't look plausible.

A black hole is the same as a collapsar.  "Collapsar" was proposed on analogy 
with "quasar" and "pulsar" but it didn't catch on as well.  Maybe it's making 
a resurgence.

Earl Wajenberg

Here is the most technical documentation I have on rotating black holes,
wormholes, white holes, and passages to other universes:

	The central singularity of a rotating black hole is very
	complicated, and the final stages of collapse are not well
	understood.  It seems conceivable that some kind of 
	re-explosion might occur but this is most peculiar, 
	because the expaning object could reach some given r[adius]
	at the same time as the contracting object!  In other
	words matter could have closed *timelike world-lines*
	-- a gross violation of causality.  One bizarre possible
	way out of this dilemma is suggested by the mathematics:
	the expansion occurs into `another' universe (related to
	our own like the positive and negative `branches' of the
	square root function).  Objects exploding through their
	Schwarzchild radii would behave like time-reversed black
	holes, and hence are called *white holes*.  It is sug-
	gested that some supernovae might be white holes, pro-
	duced either by collapse of a black hole in another
	universe or by the delayed explosion of bits of matter
	left over from the big bang at the birth of this universe.

	-- Michael Berry, Principles of Cosmology and Gravitation
	   Cambridge University Press, 1976

The same book a couple of pages before mentions the way large rotating
masses could noticably affect space by their rotation -- they "drag" the 
nearby inertial frames around with them.

A while back, I mentioned that Kurt Goedel found a solution of GTR's field 
equations in which time travel becomes possible if the material universe as a 
whole is rotating.  Goedel discussed this in "An Example of a New Type of 
Cosmological Solution of Einstein's Field Equations of Gravitation," Reviews 
of Modern Physics, 21 (1949)

Earl Wajenberg

    	Keeping this in the context of collapsars, HOW IS time travel
    possible by using the forces in a collapsar, according to the report
    you mentioned.
    
    	Larry
    

Re .24:

> Given their usefulness in explaining quasars and X-ray stars, black holes 
> aren't much more "mythical" than neutron stars or quarks.  (These have never 
> been directly observed either.)  The singularities at their centers are, I
> grant you, more conjectural and a firm belief in their existence shows a 
> touching faith that GTR is the Final and Absolute Truth, a commodity science 
> does not typically deal in.

	Black holes (defined as objects with Schwarzchild singularities) are 
not necessary to explain quasars or X-ray stars.  Further, if you look at 
Einstein's general theory of relativity, you find that black holes are a 
limiting case, not a real phenomenon.  Belief in Einstein's general theory of 
relativity does not require the belief in black holes.  In fact, a belief in 
the existence of black holes shows a lack of knowledge of the details of 
Einstein's theory of general relativity.

Re .25:

>	The central singularity of a rotating black hole is very
>	complicated, and the final stages of collapse are not well
>	understood.

	There are several problems with the statement.  It fails to take into 
account the fact that the singularity is a mathematical artifact, not a real 
phenomenon.  If the object under discussion is a star undergoing 
gravitational collapse, no singularity is involved and enough material to 
account for the angular momentum will be expelled during the collapse.

>	...........  It seems conceivable that some kind of 
>	re-explosion might occur but this is most peculiar, 
>	because the expanding object could reach some given r[adius]
>	at the same time as the contracting object!  In other
>	words matter could have closed *time-like world-lines*
>	-- a gross violation of causality.  One bizarre possible
>	way out of this dilemma is suggested by the mathematics:
>	the expansion occurs into `another' universe (related to
>	our own like the positive and negative `branches' of the
>	square root function).  Objects exploding through their
>	Schwarzchild radii would behave like time-reversed black
>	holes, and hence are called *white holes*.

	Again the invocation of the Schwarzchild solution without reference 
to the special conditions under which it applies.

>	..........................................  It is sug-
>	gested that some supernovae might be white holes, pro-
>	duced either by collapse of a black hole in another
>	universe or by the delayed explosion of bits of matter
>	left over from the big bang at the birth of this universe.

>	-- Michael Berry, Principles of Cosmology and Gravitation
>	   Cambridge University Press, 1976

	The whole section is based on a misunderstanding of the limitations 
of the Schwarzchild solution.

> The same book a couple of pages before mentions the way large rotating
> masses could noticeably affect space by their rotation -- they "drag" the 
> nearby inertial frames around with them.

	This is much more standard and does come out of Einstein's general 
theory of relativity with a little effort.  It is known as Mach's (sp?)
principle and Einstein admitted to be a follower of Mach. 

> A while back, I mentioned that Kurt Goedel found a solution of GTR's field 
> equations in which time travel becomes possible if the material universe as a 
> whole is rotating.  Goedel discussed this in "An Example of a New Type of 
> Cosmological Solution of Einstein's Field Equations of Gravitation," Reviews 
> of Modern Physics, 21 (1949)

	The assumption that the universe might be rotating is very weak.  The 
known size and density put it in the class of objects that suffer from 
gravitational collapse, if it has not already collapsed.  Such objects shed 
their angular momentum before they collapse.

	It is even possible that the universe exists inside a singularity of
the Schwarzchild variety. One of the things about such singularities is that
they have internal and external properties.  Internal properties effect
things inside the singularity and have no effect on anything outside the
singularity.  External properties effect things outside the singularity and
have no effect on anything inside the singularity.  Net charge and angular
momentum are external properties according to the usual analysis. 

    re .27:
    
    I'd like to see a definition of "singularity".
    Are you equating "singularity" with "black-hole"? 
    
    re Mach's Principle:
    
    As I remember, Mach's Principle results from the following experiment.
    
    take a bucket, fill it partially full with water.
    now spin the bucket though the long axis.
    the surface of the water will form a "bowl" and climb up the sides
    of the pail.
    now repeat the experiment except this time hold the bucket still
    and rotate the universe around it.
    the forces on the water appear exactly the same, so the water does
    the same thing.
                                                      
    The conjecture being that if you were to put a very massive torus
    around the bucket and spun it(the torus), the water would again climb 
    up the sides. This also implies that unlike an electro-magnetic solenoid,
    the field across the hole is not uniform. And in fact is zero along
    the center-line.
    
                                                   
                  /
                 (  ___
                  ) ///
                 /
    
    
    

    What follows is excerpted from _Gravitation_ by Charles W. Misner, Kip
    S. Thorne, and John Archibald Wheeler (W. H. Freeman and Company, New
    York: 1973), pages 817 to 940.  (The book is 1279 pages, a little light
    reading.) 

    There is no equilibrium state at the endpoint of thermonuclear
    evolution for a star containing more than about twice the number of
    baryons in the sun. 

    What is the fate of a star that fails to eject its excess baryons
    before nearing the endpoint of thermonuclear evolution?  For example,
    after a very massive supernova explosion, what will become of the
    collapsed degenerate-neutron core when it contains more than [the
    maximum number of baryons]?  Such a supercritical mass cannot explode,
    since it is gravitationally bound and it has no more thermonuclear
    energy to release.  Nor can it reach a static equilibrium state, since
    there exists no such state for so large a mass.  There remains only one
    alternative; the supercritical mass must collapse through its
    "gravitational radius," r = 2M, leaving behind a gravitating "black
    hole" in space. 

    To determine whether the spacetime geometry is singular at the
    gravitational radius, send an explorer in from far away to chart it.
    For simplicity, let him fall freely and radially into the gravitational
    radius, carrying his orthonormal tetrad with him as he falls [I never
    leave home without it]. 

    Of all the features of the traveler's trajectory, one stands out most
    clearly and disturbingly:  to reach the gravitational radius, r = 2M,
    requires a finite lapse of proper time, but an infinite lapse of
    coordinate time:  [equations].  Of course, proper time is the relevant
    quantity for the explorer's heart-beat and health. 

    The payoff of this calculation:  according to equations (31.6), none of
    the components of RIEMANN in the explorer's orthonormal frame become
    infinite at the gravitational radius.  The tidal forces the traveler
    feels as he approaches r = 2M are finite; they do not tear him apart --
    at least not when the mass M is sufficiently great . . .  The
    gravitational radius is a perfectly well-behaved, nonsingular region of
    spacetime, and nothing can prevent the explorer from falling on inward. 

    By contrast, deep inside the gravitational radius, at r = 0, the
    traveler must encounter infinite tidal forces, independently of the
    route he uses to reach there.  One says that "r = 0 is a physical
    singularity of spacetime."  To see this, one need only calculate from
    equation (31.4b) or (31.6) the "curvature invariant":  I . . . = 48
    M^2/r^6. 

    [Exercise 31.1b reveals the mass of the black hole required to permit a
    human to pass the gravitational radius without being mutilated is
    approximately one thousand times the mass of the sun.] 

    What does it mean for r to "change in character from a spacelike
    coordinate to a timelike one"?  The explorer in his jet-powered
    spaceship prior to arrival at r = 2M always has the option to turn on
    his jets and change his motion from decreasing r (infall) to increasing
    r (escape).  Quite the contrary is the situation when he has once
    allowed himself to fall inside r = 2M.  Then the further decrease of r
    represents the passage of time.  No command that the traveler can give
    to his jet engine will turn back time.  That unseen power of the world
    which drags everyone forward willy-nilly from age twenty to forty and
    from forty to eighty also drags the rocket in from time coordinate r =
    2M to the later value of the time coordinate r = 0. 

    At r = 2M, where r and t exchange roles as space and time coordinates,
    g[tt] [a "g" with a subscript of "tt"] vanishes while g[rr] is
    infinite.  The vanishing of g[tt] suggests that the surface r = 2M,
    which appears to be three-dimensional in the Schwartzsrchild coordinate
    system, has zero volume and thus is actually only two-dimensional, or
    else is null . . . 

    [The text explores problems with coordinate systems.] . . .  Thus there
    are actually _two_ singularities, not one, . . .  Thus there are
    actually _two_ exterior regions, . . .  How can this be? . . .  The
    answer must be that the Schwarzschild coordinates cover only part of
    the spacetime manifold; they must be only a local coordinate patch on
    the full manifold. 

    Exercise 31.4  HOW LONG TO LIVE?  Show that once a man falling inward
    reaches the gravitational radius, no matter what he does subsequently
    (no matter in what directions, how long, and how hard he blasts his
    rocket engines), he will be pulled into the singularity and killed in a
    proper time of tau < tau[max] = pi M = 1.54*10^-5 (M/M[sun]) seconds.
    [If you fall into the 1000 suns black hole mentioned earlier, you will
    live at most 1/65 seconds, your time.] 

    [I think this passage describes the Schwarzschild geometry when no star
    is present to generate it.]  Qualitatively speaking, the two
    asymptotically flat universes begin disconnected, with each one
    containing a singularity of infinite curvature.  As the two universes
    evolve in time, their singularities join each other and form a
    nonsingular bridge.  The bridge enlarges, until it reaches a maximum
    radius at the throat of r = 2M.  It then contracts and pinches off,
    leaving the two universes disconnected and containing singularities
    once again.  The formation, expansion, and collapse of the bridge occur
    so rapidly, that no particle or light ray can pass across the bridge
    from the faraway region of one universe to the faraway region of the
    other without getting caught and crushed in the throat as it pinches
    off. . . .  It turned out to represent a "wormhole" connecting two
    asymptotically flat universes. . . .  As a solution to Einstein's field
    equations, this expanding and recontracting wormhole must be taken
    seriously.  It is an exact solution; and it is one of the simplest of
    all exact solutions.  But there is no reason whatsoever to believe that
    such wormholes exist in the real universe!  They can exist only if the
    expanding universe, ~ 10^10 years ago, was "born" with the necessary
    initial conditions -- with "r = 0" Schwarzschild singularities ready
    and waiting to blossom forth into wormholes.  There is no reason at all
    to believe in such pathological initial conditions! 

    There is no possible way for any gravitational influence of the radial
    collapse to propagate outward. 

    Hence, to the distant astronomer, the collapsing star appears to slow
    down as it approaches its gravitational radius:  light from the star
    becomes more and more red-shifted.  Clocks on the star appear to run
    more and more slowly.  It takes an infinite time for the star to reach
    its gravitational radius; and, as seen by the distant astronomer, the
    star never gets beyond there. 

    [Someone falling into the singularity at r = 0 will suffer unlimited
    stretching between head and foot but greater crushing from all sides.] 

    Does this basic picture -- instability, implosion, horizon, singularity
    -- have any relevance for real stars?  Might complications such as
    rotation, nonsphericity, magnetic fields, and neutrino fluxes alter the
    qualitative picture?  No, not for small initial perturbations from
    sphericity.  Perturbation theory analyses described in Box 32.2 and
    exercise 32.10 show that _realistic, almost-spherically symmetric
    collapse, like idealized collapse, is characterized by instability,
    implosion, horizon;_ and Penrose proves that _some type of singularity
    then follows_. 

    Highly nonspherical collapse is more poorly understood, of course.
    Nevertheless, a number of detailed calculations and precise theorems
    point with some confidence to two conclusions:  (1) horizons (probably)
    form when and only when a mass M gets compacted into a region whose
    circumference in EVERY direction is @ <= 4 pi M; (2) the external
    gravitational field of a horizon (black hole), after all the "dust" and
    gravitational waves have cleared away, is almost certainly the
    Kerr-Newman generalization of the Schwarzschild geometry.  If so, then
    the external field is determined uniquely by the mass, charge, and
    angular momentum that went "down the hole".  (This nearly proved
    theorem carries the colloquial title "A black hole has no hair.") 

    Of course, the settling down involves dynamic changes of the fields and
    an associated outflow of gravitational and electromagnetic waves.  And,
    of course, the outflowing waves carry off mass and angular momentum
    (but not charge), there by leaving M [mass] and S [angular momentum]
    changed.  And, of course, the external fields must then readjust
    themselves to the new M and S.  But the process will quickly converge,
    producing a black hole with specific final values of M, Q [charge], and
    S and with external fields uniquely determined by those values. 

    A Schwarzschild black hole is "dead" in the sense that one can never
    extract from it any of its mass-energy. 

    A Kerr-Newman black hole -- which is rotating or charged or both -- is
    not dead.  The rotational and electromagnetic contributions to the
    mass-energy _can_ be extracted.  By a suitable arrangement of external
    apparatus, one can trigger an exponentially growing energy release.
    But for a perturbed black hole in isolation, the release is always
    "controlled" and damped; i.e., Kerr black holes are stable in any
    classical context. 

    Accretion and emission of x-rays and gamma-rays:  Gas surrounding a
    black hole gets pulled inward and is heated by adiabatic compression,
    by shock waves, by turbulence, by viscosity, etc.  Before it reaches
    the horizon, the gas may become so hot that it emits a large flux of
    x-rays and perhaps even gamma-rays. 

    A lump of matter falling into a black hole should emit a burst of
    gravitational waves as it falls.  The total energy radiated is E ~ .01
    mu (mu/M), where mu is the mass of the object. 

    By a non-Newtonian, induction-zone gravitational interaction, a black
    hole gradually transfers its angular momentum to any
    non-axially-symmetric, nearby distribution of matter or fields.
    [Magic!] 

    A star or planet falling into a large black hole will get torn apart by
    tidal gravitational forces.  If the tearing occurs near but outside the
    horizon, it may eject a blob of stellar matter that goes out with
    relativistic velocity ("tube-of-toothpaste effect").  Moreover, the
    outgoing jet may extract a substantial amount of rotational energy from
    the hole's ergosphere -- i.e., the hole might throw it off with a rest
    mass plus kinetic energy in excess of the rest mass of the original
    infalling object. 

    When two black holes collide and coalesce, the surface area of the
    final black hole must exceed the sum of the surface areas of the two
    initial black holes . . . 

    [The text goes into the mathematics of frame dragging.] 


				-- edp                     

Re .28:

	I stuck a definition of singularity in either this note or in the 
"myths" note where it started.  I hate to repeat myself.

	It is not me that is equating singularity with black hole, but common 
usage.  There are other ways of looking at the situation, but the equivalence 
is the most prevalent.

	The way I heard the Mach experiment described was much the same, but
had some minor variations - There was no explicit mention of spinning the
universe and the conjecture was that the water would ignore the fact that the
bucket was rotating if the walls of the bucket were made thick enough. 

    a few corrections:
    
    Hawking did NOT write "Fuzzy Black Holes Have No Hair", Jerry Pournelle
    did, based on a lecture by Hawking in which he presented the paper
    "Black Holes Aren't Black".
    
    The equation for the Scharzschild radius is:
    
    			r = 2GM/c�   (c^2 if you don't have a VT2xx)
    
    BTW the first speculation about a body with an escape velocity greater
    	than the speed of light was done by LaPlace back in 1799!
    
    "On the other hand, if a star ... is rotating fast enough, some
    solutions to the Einstein tensor suggest that the singularity formed
    will be a donut; you could dive through that and come out in one
    piece, provided the donut were large enough.
    	"Large enough means galactic sized...what you come out to on
    the other side is not according to the equations, our universe at
    all."
    	-Jerry Pournelle, "Black Holes and Cosmic Censors"
    
                                                   
                  /
                 (  ___
                  ) ///
                 /
    
     

    I don't recall seeing any discussion of the mechanism for Hawking's
    theory of black hole decay, so here is a Sunday-supplement summary:
    
    The densities of the gravitational field energies near the event
    horizon of a black hole are high enough to supply the needed energy
    for the production of particle/anti-particle pairs.  When these
    pairs are produced, one member falls into the hole while the other
    one flies out into open space.  The net effect is to soak energy
    out of the black hole.
    
    Since it is completely random which particle comes flying out, half
    the particles will be matter and half will be antimatter.  They
    will combine with each other to produce X-rays or various exotic
    particles that continue to intercombine until THEY produce X-rays,
    gamma rays, and assorted neutrinos.
    
    The smaller the black hole is, the faster it evaporates in this
    way.  Star-sized ones are very slow.  Notice that you created the
    black hole with a large load of almost pure matter and you get out
    half matter and half antimatter.  This violates baryon conservation,
    but them's the breaks.
    
    Earl Wajenberg

    	I would REALLY like to know how it might be possible for a manned
    starship to someday use the gravitational forces of a collapsar
    to reach other universe, other points in our Universe, and commit
    time travel - all without killing the crew.
       
    	Do you need to approach a collpasar at a certain angle, or have
    a specially-structured starship, or both, or what?
    
    	Larry
    

    Given the things I have read in previous notes, I think you would
    have to find a black hole big enough to not tear the ship apart
    with tidal stresses.  The nearest place to find one would be the
    center of our galaxy, a mere 30,000 light years away.  It would
    undoubtedly be surrounded by a frantically intense radiation storm,
    too.
    
    Yes, you need to follow a certain path inside the hole.  Given what
    Misner, Thorne, and Wheeler said about wormholes closing instantly,
    you might also need sf super-widgets to force it open again.  Something
    in the way of an antigravity generator, I'd suppose.
    
    Also, all this assumes that general relativity goes right on working
    right up to infinite densities.  In most other theories, when
    singularities show up they decide something is wrong or at least
    inadequate in the theory.
    
    Turning into a more science-fictional vein, I would suggest that
    the bizarre dimensional tricks of general relativity give the sf
    author a great excuse for a technology that does the same thing,
    only more quietly, efficiently, and on a smaller scale.  That is,
    the author could use GTR as a rationalization for the operation
    of his hyperdrive, time machine, or dimension hopper.  You'd use
    an imaginary advance of physics and technology to supply you with
    some form of artificial gravity which, with careful tinkering, produces
    some of the bizarre effects of a black hole in miniature, rather
    the way a fusion reactor reproduces some of the effects of a star
    in miniature.
    
    Earl Wajenberg

    	The October, 1986 issue of ASTRONOMY magazine has an excellent
    article on collapsars, detailing the four main theoretical types.
                                                  
    	Larry
    

Associated Press Tue 07-OCT-1986 09:55                           Quasar Finds

        New Quasars That Throw Giant Cosmic Blobs Found 
 
  LOS ANGELES (AP) - Scientists watching the celestial objects
known as quasars have spotted giant blobs of cosmic material
shooting from seven of them, doubling the number of quasars known to
behave that way.
   The find, announced Monday, adds support to the theory that at
the heart of every quasar lies a black hole.
   The scientists used a network of radio telescopes in the United
States and Europe to study 67 quasars and radio galaxies. Quasars
are immensely bright objects near the distant fringes of the
universe. Radio galaxies are those which emit more energy as radio
waves than as light.
   During two recent periods of observation, they saw seven of the
quasars throw out jets of material trillions of miles long at nearly
the speed of light.
   Anthony Readhead, director of the California Institute of
Technology's Owens Valley Radio Observatory and the leader of the
team that made the discovery, said the scientists owe part of their
success to good timing.
   ``You have to be lucky and looking at it when it shoots out a new
                                                            More -->
Associated Press Tue 07-OCT-1986 09:55                  Quasar Finds (cont'd)

blob,'' he said.
   The discoveries bring to 14 the number of quasars known to emit
such jets of material. Readhead said he expects the number to rise
substantially as the experiment continues.
   As many as half of the quasars under observation could display
such characteristics, he speculated.
   Quasars are so far away that they should be almost invisible, yet
so bright that for many years astronomers thought they were nearby
stars.
   For years scientists have sought to understand what the source of
energy is for these relatively small objects that are five to 10
billion light years away from Earth.
   In 1969, for the first time, scientists observed that one quasar
was sending off material that was traveling so fast it had to be
moving at near the speed of light.
   That led some to speculate that the power that drives the quasar
must be a black hole. Such holes are believed to be the extremely
dense remnants of collapsed stars, with a gravitational pull so
strong that not even light can escape.
   For material to escape the black hole, it would have to be spun
                                                            More -->
Associated Press Tue 07-OCT-1986 09:55                  Quasar Finds (cont'd)

off from the outer edge of the quasar, and it would have to be
traveling at near the speed of light in order to escape the black
hole's gravitational field.
   That led to a flurry of excitement among astronomers who believed
that if the speculation were correct, it should be relatively easy
to find quasars that are sending off speedy jets of material, most
likely the debris from stars that were sucked into the gravitational
field and then disintegrated.
   In the following years, six more quasars were found to be
spitting out jet streams at speeds near that of light.
   Readhead said if such activity is common, that lends credence to
the theory that quasars are most likely powered by black holes.
That, in turn, could help scientists understand some of the most
fundamental driving forces in the universe.
   Many astronomers believe a black hole lies at the heart of every
galaxy.

      From the October 14, 1986 edition of Vogon News -

    Astronomers at the new La Palmaobservatory in the Canary Isles have
    carried out observations that can only be done once every 19 years.
    The position of what is believed to be a black hole at the centre of
    the galaxy was examined by using the moon as a shutter and observing
    the infra-red radiation from the dust cloud surrounding the object.

      Does anyone have any more information on this observation?

      Larry

It occurs to me that, thanks to Hawking radiation, black holes may be 
impossible to break into.  If you try, you should take a good radiation 
screen.

According to Steven Hawking's theory, any black hole will eventually evaporate 
thanks to quantum mechanical effects.  The time is horribly long, but finite. 
Now consider an observer falling into a black hole.  From our point of view, 
his clocks run slower and slower as he approaches the event horizon, 
asymptotically apporaching a dead halt.  (Please note that this kind of time 
distortion is NOT relative, as is the time distortion of two frames in 
relative motion.)  Meanwhile, as he falls, the black hole produces a small but 
exponentially increasing drizzle of Hawking radiation.

From his point of view, things are much livelier.  As he falls toward the 
event horizon, the starlight behind him blue-shifts insanely into the 
ultraviolet, X-ray, and gamma.  And the Hawking radiation is not a negligible 
drizzle.  Instead, it increases rapidly.  The event horizon shrinks away from 
him as he falls toward it, as the black hole's mass is boiled away in equal 
quantities of matter and antimatter, which would be annihilating all around 
the observer.  More gamma rays.  In short order, the radiation builds up to a 
single intense explosion and our well-shielded observer finds he is in open, 
undistorted space with no black hole around.  Also no stars.  They all burned 
out long ago, and the date is something like ten to the 100th.

I don't know how all this would look to an observer stationed on the surface 
of the star as it started to form into a black hole, but I think it would be 
similar.  (The observer had better be able to cope with several thousand 
gravities.  Perhaps he could be a piece of intelligent neutronium like the 
creatures in Forward's "The Dragon's Egg.")  It might be that singularities 
never form in the bottom of a black hole because, on an outside timescale, 
they take forever to form and the black hole evaporates before then.  (On an 
inside timescale, they form quickly but the hole evaporates even more 
quickly.)

Earl Wajenberg

Newsgroups: sci.space
Path: decwrl!decvax!ucbvax!ucbcad!ames!lll-lcc!seismo!mnetor!utzoo!utgpu!water!
Subject: Re: frozen stars
Posted: 3 Apr 87 18:43:06 GMT
Organization: U. of Waterloo, Ontario
 
    In article <870402092920.00001A93.AJFE.VE@UMass> [email protected] 
(Andy R. Steinberg) writes: 

>The is one thing that has been bugging about black holes for a long
>time. A black hole can only have 3 properties, mass, charge, and
>rotation. A static black hole has 1 event horizon, whereas a charged
>or rotating black hole has 2 event horizons. I don't understand how
>there can be 2 places where time stops(relative to an outside
>observer) and the escape velocity = c. I have heard somewhere that
>the outer event horizon is the ergosphere, but I don't know what
>an ergosphere is and can't find any reference to it.
 
At the risk of doing a gross oversimplification:
An event horizon is a boundary through which you cannot come back:
  i.e. any thing that goes in cannot go out even light (hence the
  black in the name Black hole).
 
The ergosphere is somewhat different. It is a region in which you
 cannot stand still with respect to (say) the distant stars.
 Let me elaborate a bit.
 
A non-rotating black hole (the first type that was discovered )
 has an event horizon : anything that goes in cannot come out.
 You can, however, stand still w.r.t. the distant stars, provided
 you are outside the event horizon.  It will take some expenditures
 in energy though, you have to counterbalance gravity. It is like
 stopping a satellite in the sky - i.e. prevent it from orbiting -
 and yet keep the rockets firing to prevent the satellite from falling
 down.
 
For a rotating black hole however, things are a bit more interesting.
 You still have an event horizon, as before, but this time it is
 distorted a bit as compared to the non-rotating BH. -- nothing magic
 here, it is similar as to why the Earth has a bulge, you can think
 of it as the effect of the centrifugal force. There is something new
 in this case however.  Remember the picture associated with a BH,
 i.e. that of a ball distorting a sheet of rubber -- hence the popular
 "gravity wells" that are sometimes printed on t-shirts. Now set
 the ball rotating around (say) the vertical axis. The rubber sheet
 is dragged along with the rotation, that is, it rotates with the ball.
 (Well up to a certain point, this is only an analogy). Something similar
 happens around a rotating black hole. The space-time is dragged along
 with the rotating black hole. Now, lets get back to that satellite,
 or rocket. Not only does it have to fight against the downward gravity
 to lay still w.r.t. the distant stars, but in addition it has to fight
 against the rotation of the space-time itself.  The problem is,
 can it succeed. The ergosphere is the region where even with infinite
 energy, the rocket fails to maintain a fix w.r.t. those stars.
 Note: it does not mean that you cannot get away from the ergosphere.
 Provided you are outside the event horizon, you can still get out,
 even if you are inside the ergosphere.  As an interesting side effect,
 it also means you can steal energy from a rotating black hole, by stealing
 some of the energy stored in that rotating space-time. (You don't have
 to go in the ergosphere to do it). -- A yeah, quantum gravity also
 predicts energy can be emitted from any BH through Hawking's radiation.
 
This is already long enough. I hope this clears up a few hazy notions.
 
I choose the stars.
  
-- 
Je'ro^me M. Lang	   ||    [email protected]        [email protected]
Dept of Applied Math       ||			  jmlang%[email protected]
U of Waterloo		   ||  	 jmlang%water%[email protected]

VNS MAIN NEWS:                            [Richard De Morgan, Chief Editor, VNS]
==============                            [Basingstoke, England                ]

    Science, Technology, Medicine, and Nature
    -----------------------------------------

    It has been confirmed that black holes lie at the center of Andromeda
    Galaxy (M31) and a smaller galaxy, M32.

  <><><><><><><>   VNS Edition : 1515    Thursday 25-Feb-1988   <><><><><><><>

    Well, if it says so in VOGON, it's *gotta* be true!!
    
    					(-: andrew :-)

    	I would much rather have a more authoritative source myself,
    but VNS is the first place I read this.  If anyone has more details
    on this (Does this *confirm* the existence of black holes?), please
    post it here.
    
    	Larry
    

    My own guess is that someone has sighted an intense X-ray source at the
    center of the Andromeda galaxy, and current theory has it that such
    things are black holes, hence the headline.
    
    Earl Wajenberg