Re: can anything at all fall into a black hole?
From: MP (pet.antispam_at_onlinehome.de)
Date: 11/24/04
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Date: Wed, 24 Nov 2004 18:11:32 +0100
"Dr. Photon" <brendan.roycroft@nmrc.ie> wrote in message
news:b8f632e2.0411240606.44c90587@posting.google.com...
> "MP" <pet.antispam@onlinehome.de> wrote in message
news:<cnogm9$jfk$1@online.de>...
> > "plex" <felix_arnold@hotmail.com> wrote in message
> > news:307dusF2q5j2lU1@uni-berlin.de...
> > > hi folks
> > >
> > > I wonder if anything can fall into a black hole rather than just stay
> > > at the event horizon.
> >
> > This is a good question. From the outside it appears, that nothing
> > is ever going to reach the event horizon.
> >
>
> Follow up problem: So when does the event horizon increase its
> apparent diameter?
Good question. Conventional wisdom says that the event horizon
moves acausally, already in anticipation of the matter that will
fall into it in the future.
> If according to the outside observer, the object has not fallen in to
> the black hole, then the mass of the black hole has not increased.
Right, but the mass is still there, and you will not be able to
differentiate between the mass *in* the black hole and the mass
slightly outside. What you measure outside is the combined
gravitational effect. And then the event horizon starts to move
outward, even if the matter has not yet passed it (see above)
> However, it is said that the event horizon radius is proportional to
> the amount of matter that has fallen into the black hole.
See above. And then:
The classical black hole solutions aren't very well suited to
analyze any dynamic problem, with real matter falling in. The
solution describes a completely stationary state. Most believe
that the stationary black hole remains a good approximation
even when particles fall into a black hole. However, in GR one
has to be very careful with approximations.
> So, from the external point of view, (which is the important one to
> someone in the vicinity of the hole!) at what time does the event
> horizon increase?
In order to answer that, you have to know the whole space-time's
future. At least this is what conventional black hole physics says.
It doesn't mean that the conventional point of view is right. I
don't believe that event horizons, trapped surfaces or "large"
classical space-time singularities are realized in the real physical
world. These are mathematical solutions to the field equations.
Most mathematical solutions of the field equations are physically
nonsense. I am convinced, that the physical realized solutions
are (most likely string type) solutions of the field equations without
singularities. One such solution is the holographic solution:
ds^2 = r0/r dt^2 - r/r0 dr^2 - r^2 d \Omega
r0 is of order Planck length.
The above solution has high potential. Of course nobody except
MP finds this solution interesting enough to waste one's time to
study it. And surely MP must be crazy to study a classical solution
of GR without singularities (and with string-type interior matter), as
everybody knows, that singularities, trapped surfaces etc. are
generic features of the mathematical solutions of GR. And surely
*any* generic mathematical feature must be realized physically?!
But is this reasoning really sound? IMO it is probabilistic
reasoning by numbers: Most solutions we found so far have
event horizons, singularities etc. Furthermore the singularity
theorems show, that singularities are generic. So we believe
that most physically realized solutions will have these generic
features. OTOH the only physically realized solutions from
which we know that they actually exist in nature (neutron
stars, "normal" relativistic stars, etc.) *don't* have any
singularities.
Therefore MP proposes the following innocent thesis:
Knowing that most mathematical solutions of GR are nonsense
(you can construct *any* solution you want just by postulating
a completely arbitrary metric and calculate the stress-energy
tensor that follows from this metric), there must be some
- yet unknown - selection principle that projects out the (few)
physical solutions out of the vast space of mathematical
solutions that make no sense. What if this physical "projection
operator" eliminates most of the generic mathematical features
of the solutions, such as singularities, trapped surfaces,
event horizon etc. ?! Is this absolutely unthinkable?
If it is not, we might have a serious problem, don't you think?
It is not MP's problem, though.
Best MP
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