Stars collapsing to form a black hole
Mike_Fontenot
I've just finished working my way through Dirac's two chapters on the
derivation of the Schwartzchild metric, and on its implications for
black holes. At the end of the second chapter, he says that a star
collapsing in on itself, and forming a black hole, will take an infinite
time to do so, according to a distant observer (but a finite time
according to a frame moving with the collapsing matter). That seems to
say that there should currently (for us) be no black holes anywhere in
the universe, because not enough of our time has passed to allow that.
If there ARE currently any black holes in the universe, it would seem to
be necessary that they already existed when the big bang occurred. Are
there any other alternatives that I'm missing?
Mike Fontenot
Tom Roberts
> I've just finished working my way through Dirac's two chapters on the
> derivation of the Schwartzchild metric, and on its implications for
> black holes. At the end of the second chapter, he says that a star
> collapsing in on itself, and forming a black hole, will take an infinite
> time to do so, according to a distant observer (but a finite time
> according to a frame moving with the collapsing matter).
Yes.
> That seems to
> say that there should currently (for us) be no black holes anywhere in
> the universe, because not enough of our time has passed to allow that.
This is PHYSICS, not theology. In physics, approximations are the rule, and to a
distant observer the collapsing star is observationally indistinguishable from a
black hole; this is so just a short time after it begins its final collapse. It
is also true that for matter falling into a black hole, the total is
indistinguishable from a black hole of the total mass; again just a short time
after the infall passes some point close to the horizon but well outside it.
> If there ARE currently any black holes in the universe, it would seem to
> be necessary that they already existed when the big bang occurred.
They could be present also.
> Are
> there any other alternatives that I'm missing?
Yes -- see above. There are compact, super-massive objects at the centers of
most galaxies, which are all consistent with being black holes. There is no
other sufficiently believable alternative, and now most astrophysicists call
them black holes (not merely candidates). It is not known whether they are
primordial or collapsed objects.
Tom Roberts
Oh No
>
>I've just finished working my way through Dirac's two chapters on the
>derivation of the Schwartzchild metric, and on its implications for
>black holes. At the end of the second chapter, he says that a star
>collapsing in on itself, and forming a black hole, will take an
>infinite time to do so, according to a distant observer (but a finite
>time according to a frame moving with the collapsing matter).
I didn't think this was so, but I haven't followed the calculation so I
can't be sure. Certainly it would take an infinite amount of our time
for matter to cross the event horizon of a black hole, but my
understanding is that, according to the calculation of Oppenheimer and
Snyder, for matter in a collapsing star, it is possible to achieve the
density at which the event horizon forms within a finite amount of time.
That is to say, my understanding is that this is what is meant when it
is said that they showed that black holes can form.
>That seems to say that there should currently (for us) be no black
>holes anywhere in the universe, because not enough of our time has
>passed to allow that. If there ARE currently any black holes in the
>universe, it would seem to be necessary that they already existed when
>the big bang occurred. Are there any other alternatives that I'm
>missing?
>
Of course, as Tom remarks elsewhere, observationally it is largely
academic. There are many objects observationally indistinguishable from
a black hole, and it is shown that the density of matter at the centre
of the galaxy is sufficient that the object must be, in effect, a black
hole.
However I don't actually believe you can push the equations of general
relativity that far. I have reasons, within relational quantum gravity,
for thinking that the event horizon is actually a physical boundary
beyond which the standard equations of gtr do not apply (notwithstanding
the indisputable fact that if they did apply they would have non-
singular solution).
Regards
--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)
Theo Wollenleben
>
> a star collapsing in on itself, and forming a black hole, will take
> an infinite time to do so, according to a distant observer (but a
> finite time according to a frame moving with the collapsing matter).
> That seems to say that there should currently (for us) be no black
> holes anywhere in the universe, because not enough of our time has
> passed to allow that.
This is related to the frequent question if a body falling into an
existing black hole will ever cross the event horizon according to a
distant observer. This question is ill-posed, since there is no
coordinate-independent concept of simultaneity. According to general
relativity the event when the body reaches the horizon should exist and
has finite proper time for the falling body. As a distant observer you
ask what your clock shows the moment this event occurs. But your
question requires a definition of simultaneity. If you use Schwarzschild
time to define it, your time tends to infinity as the body approaches
the horizon.
Tom has already pointed out that after a certain finite time a distant
observer can't receive any information from the falling body. Then it
makes sense to say that the body is inside the black hole. See also
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html
Mike_Fontenot
> See also
> http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html
>
Thanks for that link, Theo.
Mike Fontenot