At 08:06 PM 8/13/01, you wrote:
>Rodent of Unusual Size wrote:
> >
>
> >If I have done the math correctly,
> >
>You mean, R = 2GM/c^2?
>
> >the gravitational radius
> >for a mass of 4x10**26kg is about 0.62m.
> >
>0.59m
>
> >So if you managed to
> >shoehorn that much mass into a cubic metre, it would collapse,
> >yes?
> >
>Dunno, the gravitational properties of this cube would
>be complex... To be safe, compress inside a 1 meter diameter
>sphere :-)
>
> >(Leave aside for the moment my suspicion that you would
> >have long previously passed the gravitation radius for a smaller
> >mass, and would hence be feeding a singularity already.. I
> >sense a Zeno factor here. ;-)
> >
>No, because for a fixed density the mass increases with
>R^3 and the Schwarzschild Radius is proportional to the
>Mass, so that the singularity wouldn't be reached before
>you compressed more than the Sch. Radius.
>
> >Now if it collapses, what becomes the significance of the
> >gravitational radius? It is a property of mass, not volume,
> >so it should not change. Does it define the event horizon?
> >
>Yes.
>
> >That seems elegant, but I do not see that the collapse of a
> >mass and the escape velocity of that mass really have much to
> >do with each other.
> >
>They don't - but it's interesting that this Radius is the same
>that can be calculated by the classical mechanics formula :-)
>
> >Or is that part of the definition of
> >gravitational collapse? (Hmm. Is it possible for a macroscopic
> >mass [i.e., one too diffuse to fit within its own gravitational
> >radius] to be great enough to have that high an escape velocity?)
> >
>Sorry. I don't understand what you mean by this.
I think the question may be "Is it possible for an object with a radius r >
2GM/c^2 to have v(esc) > c?"
Is that a correct reading?
> >So if the mass has collapsed to the proverbial point, and the
> >R(g) has not changed.. what is the state of things in the space
> >between the centre point and the radius? Or is that a meaningless
> >question, or at least one to which there is no answer in English?
> >
>What happens for someone _outside_ the collapse is that you
>_never_ see the collapse - because there's also a time-dilatation
>phenomenon, so that you continue receiving information but never
>information of _the_ collapse.
>
>If you are inside, then forget the rest of the Universe - but you
>also won't see anything [except a huge tidal force trying to
>rip you off]
>
> >Why would not the mass of a black hole within another body
> >contribute to that body's gravity?
> >
Are you talking about the idea used in some SF stories of a mini-black hole
being trapped inside an asteroid, or do you have a mental picture of the
interior of black hole consisting of the singularity at the center
surrounded by some sort of physical barrier at r = 2GM/c^2?
>But it does! The mass [and the charge, and the angular momentum]
>never vanishes.
>
> >Why do they remain two
> >discrete systems? Or do they?
> >
>They don't remain two discrete systems - a black hole has no hair :-)
Neither do some of the experts on them, except on their chins ;-)
>Alberto Monteiro
>
>PS: a caveat: I am *not* an authority in GR...
Perhaps not, but thank you for giving the answer.
I was too tired when I read the questions to answer anything that required
more than one line, so I was going to perhaps respond tomorrow if no one
beat me to it. Not that I claim to be an "authority," by any means . . .
--Ronn! :)
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I always knew that I would see the first man on the Moon.
I never dreamed that I would see the last.
--Dr. Jerry Pournelle
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