A question about Black Holes
Jonathan M Lennox
Reply-To: jm...@cunixa.cc.columbia.edu (Jonathan M Lennox)
Organization: Columbia University
I asked this question during the summer, but didn't really receive a
satisfactory answer. I hope now that the semester's well underway I
can get some better responses.
As I understand it, from the point of view of someone "outside" a
black hole (that is to say, a person observing from a position where
space is asymptotically flat) an object falling into a black hole
appears to undergo time dilation, with time passing more and more
slowly and the object falling closer and closer to the event horizon,
never actually reaching it. However, from the point of view of
someone falling into the BH, the event horizon passes unnoticably, but
time as viewed in the rest of the universe appears to pass more and
more quickly.
Now, given only the first part of this, what I am wondering is, how
can a black hole ever grow? It seems that anything falling into it
would not ever enter the hole until the end of time for an observer
outside the hole, so is it ever possible for the hole to grow?
Secondly, if we include Hawking radiation in this (which is supposed
to cause black holes to evaporate after some absurdly large number of
years), what happens? Does an observer falling into a BH actually see
(assuming the observer could withstand the tidal effects) it evaporate
in a burst of Hawking radiation under him, so that by the time he
actually crosses the event horizon the black hole is gone, and he
finds himself in an empty universe filled only with photons from BH
radiation and other victims the black hole accrued during the entire
lifetime of the universe?
Or is there something I'm fundamentally failing to understand here?
It seems like the descriptions of the BH I've read in popularized
accounts (I've never had a formal GR course, as is probably obvious
from this question). Can those with more training than I clear this
one up for me?
Jonathan Lennox
jm...@cunixa.cc.columbia.edu
Jose Castejon-Amenedo
jm...@CUNIXA.CC.COLUMBIA.EDU (Jonathan M Lennox) writes:
> As I understand it, from the point of view of someone "outside" a
> black hole (that is to say, a person observing from a position where
> space is asymptotically flat) an object falling into a black hole
> appears to undergo time dilation, with time passing more and more
> slowly and the object falling closer and closer to the event horizon,
> never actually reaching it. However, from the point of view of
> someone falling into the BH, the event horizon passes unnoticably,
Right, in principle. But for some black holes (Schwarzschild,
in particular) it would be possible for an observer to detect the
event horizon by local measurements.
> but time as viewed in the rest of the universe appears to pass more
> and more quickly.
Assuming a Schwarzschild black hole, this conclusion is wrong.
Electrically charged, or rotating black holes admit interior horizons
where this conclusion might hold, but that's a different matter
altogether that I will not discuss right now.
> Now, given only the first part of this, what I am wondering is, how
> can a black hole ever grow? It seems that anything falling into it
> would not ever enter the hole until the end of time for an observer
> outside the hole, so is it ever possible for the hole to grow?
The fallacy stems in the conclusion that the infalling
observer A perceives events in the asymptotic zone where another
observer B is as going faster and faster, without bounds. The best way
to see that this is wrong consists of drawing a diagram of the
Schwarzschild spacetime in Kruskal coordinates.
Doing that one will see that the last light ray received by A
from B corresponds to a perfectly finite time along B's worldline.
Ascii terminals are not very good for drawing purposes, so I'll forego
undertaking that task. The diagrams I mentioned though are present on
almost any modern textbook on GR.
Lorne Churchill
falls into a black hole you _don't_ view him or her, you view reflected (or emitted)
light which takes a long time to crawl back out of the hole. The poor faller hits the
event horizon in virtually no time at all.
--
Lorne Churchill lchu...@sirius.uvic.ca
"If you can't change your mind, are you sure you still have one?"
John C. Baez
>JC-A posted the answer in terms of space-time diagrams. In layman's terms: when someone
>falls into a black hole you _don't_ view him or her, you view reflected (or emitted)
>light which takes a long time to crawl back out of the hole. The poor faller hits the
>event horizon in virtually no time at all.
I think the poster got *that* point; as far as I could tell, he's asking,
"If it takes forever for us to *see* the fellow fall past the event horizon,
and only after he's in does the black hole appear to grow (i.e., the event
horizon grows in radius), then why doesn't it take forever for the black hole
to grow."
That is an interesting question, anyway: drop a relatively puny mass into a
black hole. As a function of time (for us observers far away), describe the
black hole's event horizon. Presumably as t -> infinity it approaches
a sphere of slightly larger radius. Anyone know the manner in which it gets
there?
Kevin Schnitzius
>JC-A posted the answer in terms of space-time diagrams. In layman's
>terms: when someone falls into a black hole you _don't_ view him or her,
>you view reflected (or emitted) light which takes a long time to crawl
>back out of the hole. The poor faller hits the event horizon in virtually
>no time at all.
It has been some time since I'v done the math but I'd like to point out
that the effects of gravity on the light are minimal until the faller is
near the event horizon. I forget the initial conditions but the faller
turned red and and faded out in less that 0.5 seconds. Of course, you
could possibly detect the red-shifted light with the special instruments
but as far as visible light is concerned, the faller disappeared as he
crossed the event horizon.
The event horizon must be beautiful from the inside with all those
photons in orbit :-)
--
Kevin Schnitzius
kschn...@encore.com
ian redmount
jb...@nevanlinna.mit.edu (John C. Baez) writes:
>[discussion of previous post, concerning FAQ about matter falling into
>black holes, omitted for brevity.]
>I think the poster got *that* point; as far as I could tell, he's asking,
>"If it takes forever for us to *see* the fellow fall past the event horizon,
>and only after he's in does the black hole appear to grow (i.e., the event
>horizon grows in radius), then why doesn't it take forever for the black hole
>to grow."
>
>That is an interesting question, anyway: drop a relatively puny mass into a
>black hole. As a function of time (for us observers far away), describe the
>black hole's event horizon. Presumably as t -> infinity it approaches
>a sphere of slightly larger radius. Anyone know the manner in which it gets
>there?
Yes, someone knows. The actual manner of the horizon's growth is
rather intriguing, and illuminating. Let's start with a simple example:
Consider a Schwarzschild black hole of mass M, into which falls a thin
spherical shell of dust (concentric with the hole) of mass dM. The spacetime
of the region between the hole and the infalling shell is the Schwarzschild
geometry with mass M; that outside the shell is Schwarzschild spacetime
with mass M+dM. When the shell has fallen to a radius of 2G(M+dM)/c^2,
which incidentally takes a finite amount of time as measured by observers
stationary near the hole, it is engulfed by the horizon of the hole
WHICH HAS GROWN OUT TO MEET IT! Thereafter the horizon remains at its
new radius.
That is, the hole's event horizon grows before and up to the infall of the
shell. Counter-intuitive though it seems, the horizon evolves
``telelogically,'' in anticipation of future events rather that in
response to past ones. This is because the event horizon is a global,
not a local, geometric feature. It is defined in terms of the behavior
of signals in the asymptotic future: It is the boundary between the regions
from which signals can and cannot escape to infinity. But escape depends
on events to the future of a signal's emission, not its past, hence the
``future-anticipating'' behavior of the horizon.
The evolution thus described is in terms of a time coordinate which is
regular on the horizon. A description in terms of distant-observer time
is hampered by the same t->infinity coordinate singularity which pops up
in every discussion of infall into black holes, which prompted the original
posting in this thread, and which has been discussed here on numerous prior
occasions. Basically, distant observers outside the shell, in Schwarzschild
spacetime of mass M+dM, see the shell contract and fade away (fast) as it
is engulfed by the horizon.
If we just drop a small mass into a hole, instead of a spherical shell,
things get even more interesting. As the mass approaches (again, working
in a sensible, i.e, regular time coordinate) the horizon grows out to
meet it, developing a tidal bulge in the process. Once the mass is
engulfed, the bulge falls back, the horizon oscillates or ``ripples,''
and gravitational radiation is emitted as the hole relaxes to a spherical
shape again. Part of the mass-energy of the dropped body goes into making
the hole grow, part into radiation, and part into center-of-mass motion.
For further detail see, e.g., ``Black Holes: The Membrane Paradigm,''
Thorne, Price, and Macdonald, eds. (Yale, 1986), and references therein.
Ian H. Redmount
John C. Baez
>falls into a black hole you _don't_ view him or her, you view reflected (or emitted)
>light which takes a long time to crawl back out of the hole.
I just want to add that "layman's terms" are not very clear when it comes
to discussing general relativity, or other branches of modern physics.
One might just as well tell the poor layman, "In fact, you never *really*
see anybody, you just view the light emitted by them which has crawled out
of their gravitational field."