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.
>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?
>
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 :-)
Alberto Monteiro
PS: a caveat: I am *not* an authority in GR...
