Re: can anything at all fall into a black hole?

From: MP (pet.antispam_at_onlinehome.de)
Date: 11/22/04 

Date: Mon, 22 Nov 2004 20:31:10 +0100

"Mitchell" <macromitch@internetCDS.com> wrote in message
news:9c3da975.0411211646.54d0585e@posting.google.com...
> "Bill Hobba" <bhobba@rubbish.net.au> wrote in message
news:<ycxnd.42262$K7.32062@news-server.bigpond.net.au>...
> > "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.
> > >
> > > According to general relativity the curvation of space-time, when
> > approching
> > > the event horizon,gets infinite.
>
> There's more Plex. Even if you use different coordinates as suggested by
> Hobba below there are a number of more paradoxes.

There are, but not those paradoxes that you think.

> Everything falling in at the event horizon is falling at the speed of
light.
> So GR is in contradiction to SR where SR says matter can't reach light
speed.

This is incorrect. You fail to realize that in GR the velocity of light is a
*local*
concept. At any space-time point you have a *local* light cone. The
velocity of any massive observer always remains within this *local* light
cone. An observer at free fall towards the event horizon always remains
*within* his local light cone.

However, when you add the infinitesimal *local* distances traveled
by a photon (or by a massive obserer for instance in an FRW-universe)
over a large curved space-time region you *can* get the impression,
that parts of the space-time (or parts of universe), which are
*not in causal contact any more* appear to move apart by
a "global" velocity, that seems to be faster than the velocity of light. But
this "global" velocity is a naive concept that doesn't take into account
the curvature of the space-time. What you are doing is to divide the sum
of the *infinitesimal* distances summed up over a *large region* of the
space-time by the time measured by *one single * observer at a *fixed
space-time point*, as if the whole space-time were *flat*. This is not
permissible for a curved space-time manifold. (and the "global" velocity
you calculate by this procedure clearly is an *observer-dependent*
concept)

> What's more important is that GR also predicts an infinite gravitational
> redshift to light. But what is light that undergoes an
> infinite redshift but energyless light? An infinite Einstein shift?
> Light of infinite wavelength?
> Dead light?
> Poppy*** you know.

There would be a problem with infinite red-shift (or blue shift), if
there were "real" mass-energy (real as contrasted to virtual particles)
at the event horizon. But there is nothing, only vacuum, at the event
horizon and therefore there is no problem.

What would the problem be? What conflict with experiment or
observations (or logic) would arise? I cannot see that you have
addressed any real problem in your above paragraph.
[except that you appear to feel uncomfortable with the words that
you yourself have created: "energyless light", "infinite Einstein shift",
"infinite wavelength", "dead light" ... - what energyless light? infinite
shift of what?, infinite wavelength of what?, death of what? - there
is no light, no mass-energy at the horizon of a classical black hole.
So to what light, or wavelengths, or whatever else are you referring
to?]

[snip ...]

> > > so why should anything cross the event-horizon and go to the center of
a
> > > black hole? what's wrong about my argumentation, or isn't it wrong?
> > >
> > > plex
>
> You are not wrong in the direction you take plex. You are right on.
>
> The question that needs to be asked is "what is the timerate inside a
black
> hole?" Bill can you answer this?

Bill can answer this. But do you want to hear his answer?

Here is the answer (and it is not really Bill's answer, it is the answer
of *any* scientist who knows the *basics* of black hole physics):

The only time-rate inside a black hole, that matters, is the proper time
*measured* by the clock of an interior observer. The interior time is
tied to the radial coordinate r. Inside the black hole's interior dr is
not a spatial interval, but a time interval (because the metric coefficients
in front of dt and dr have switched sign at the event horizon). Therefore
the passage of time within a black hole is measured by the successive
intervals of dr. Within a black hole r always decreases, so time "ends"
at the *singularity* at r=0. But time does not end at the event horizon!

> Bill if time doesn't end at the event horizon(your Kruskal CO's) then
> it is not a black hole because a black hole requires an infinite redshift
> at the event horizon. Without it you could see into a black hole.

see above

> But the infinite redshift predicted by GR is the evidence of its failure.

Maybe, but not in the sense you think.

Best MP

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