andrew b wrote:

I'm a 2nd year math student, mostly physics ignorant at this point...
I read Einstein's populist book on SR and I think I have a reasonable
handle on most of that; GR, a shaky qualitative one at best, that may
be the source of my misunderstanding.

My understanding, black hole concept is: density within a volume
increases until it reaches a point where 'light cannot escape' a shell
called the event horizon... I understand this as meaning that, to an
observer outside this horizon, the time dilation they perceive at the
'surface' approaches infinity. (This may be what I'm not
understanding).

If the above is accurate, though, the concept becomes confusing to me;
from (again) the perspective of an observer always remaining outside
the event horizon, how can anything actually 'enter' the black hole?

GR predicts exactly what you say, that an outside observer will
see something taking an infinite amount of time to reach the event
horizon.

But it also predicts that an observer that is actually falling into
the black hole will take a finite amount of time (according
to that observer's clock) to reach the event horizon.

The resolution of this requires understanding the difference
between coordinate and proper times in GR and how
spacetime curvature affects measurements made at different
events in spacetime.

See the FAQ for this newsgroup, or keep studying and take
a course in GR a few years later into your math studies.

John Anderson

andrew b wrote:

GR predicts exactly what you say, that an outside observer will
see something taking an infinite amount of time to reach the event
horizon.

But it also predicts that an observer that is actually falling into
the black hole will take a finite amount of time (according
to that observer's clock) to reach the event horizon.

The resolution of this requires understanding the difference
between coordinate and proper times in GR and how
spacetime curvature affects measurements made at different
events in spacetime.


See, thing is my problem is not at all the apparent contradiction (at
least, I don't think so... see my above response to magnus). I don't
have a problem that an observer approaching the event horixon can pass
through in a finite time even though any extrenal observer will NEVER
see her pass through the horizon... that's just a context (frame)
issue, no more hard for me to accept then events that appear
simultaneous to some will appear displaced in time to others (a
difference between 0 time between events and a finite time between
them being frame-dependant, just as the black hole situation seems to
be a difference between an inifinite time between events from one
persepctive and a finite one from another).

My problem is how an extrenal observer will percieve the incoming mass
as being 'added' to the black hole... in other words the physical
nature of black holes for everyone and everything in perpetuity
throughout existence that happens to avoid entering one. Hence my
questions (clarified in response to magnus).

Ignore the last part about mass distribution inside the singularity
(in my origainal message), I guess that's where I gave the perception
of being frame-confused... I just basically wanted to know if
conceptualizing a black hole as involving a singularity at the center
of the event horizon was at all meaningful from the context of someone
who does not ever cross the horizon.. and it seems the answer is no,
it doesn't (from magnus's response).

In any case thank you for the reply.

First of all, I think that the above is your response tome, but, I can't
be sure. Please acknowledge the author
of the posting that you're replying to so that it's easier
for us to decide which of your postings to reply to.

The outside observer won't observe the mass being
added to the black hole.

If you have a problem with that, show us an experiment
that will give a result that will disagree with that prediction.

John Anderson

John Anderson wrote in message ...

First of all, I think that the above is your response tome, but, I can't
be sure. Please acknowledge the author
of the posting that you're replying to so that it's easier
for us to decide which of your postings to reply to.

Sorry, I've acknowledged you this time. (well, obviously
In my usenet reader (I use Google groups) it automatically nests
messages visually, does usenet not actually do that? or is the problem
that someone could potentially have posted in the chain between my
post and yours and (again potentially) that post had not reached your
usenet provider yet?

The outside observer won't observe the mass being
added to the black hole.

If you have a problem with that, show us an experiment
that will give a result that will disagree with that prediction.

I get the feeling I'm being put into a neat little box reserved for
people who pervasively refuse to accept that some relativisitic
results may seem paradoxical from a stuborn intuitive perspective; I
don't think I'm one.


I don't have a problem about 'no mass being added to a black hole from
and outside perspective'... In fact the idea that mass could be added
to it (assuming no quantum influences) seems totally counterintuitive
to me.

I am not trying to contest any theory here, just trying to understand
what will happen to mass approaching the horizon from an external
perspetive. I'll try to make my questions clearer:

1: How will matter objects appear to distort as they indefinetly
approaches the horizon?

2: Specifically, will they seem to in any way become flattened or
compressed (to an outsied observer)? (i.e. seeming to have less volume
for the same ammount of mass?) If the answer here is NO, then the
questions from 3 on are withdrawn.

3: If the answer to 2 was YES, then I would concluded that from all
external perspective the matter approaching an event horizon appears
to become denser. Now: what happens when the percieved density of some
part of the infalling matter is great enough that the external
observer would expect it to form another black hole, centered on the
infalling lump under question? Does another seperate (but
intersecting) event horizon come into being? (always, always from an
outside perspective)

4: If the answer to 3 is NO, another singularity does not form, then
is the following explanation for WHY one does not correct?: In an SR
situation, I believe, an object that is moving at a great relative
velocity to you will appear to become flattened, but yet (according to
the relativity.physics.faq, which I may or may not understand), it
will never appear to you as a black hole... Presumably despite the
fact that the object appears to you be compressed to a small enough
volume(?).

5: If the explanation posed in #4 is CORRECT; in other words if the
situation of you observing an object very near a black hole is, in
fact, CONGRUENT to the SR situation of you observing a fast-moving
object IN THE CONTEXT THAT, despite the fact that the object would
appear to be very dense, it will never form a singularity, then I
think I understand what I want to understand... (to the limit of the
time when I can actually handle GR math and understand why the SR&GR
situations are congruent in this way)...

6: Just to confirm, then: an event horizon, once formed, can never
change in diameter? (again disregarding quantum effects)

Finally,
7: If the SR and GR situations I've described are NOT congrous in that
approaching mass WILL compact to form a singularity... then I am
confused, because it would seem like an event horizon would slowly
accumulate many other event horizons 'sticking out of it' like
bubbles, and so on recursively(?); this is not something I have ever
heard discussed, therefore I assume that it is wrong; perhaps said
'bubbles' would appear flattened onto the event horizon for the same
reason as matter would appear to be compacted near the horizon (?) (in
which case it might still seem to make the even horizon bumpy, just
less so); or perhaps the approaching matter would be spread out so
much before it reached critical density that the new singularities
would be centered on individual particles or clusters of particles,
making the black hole 'simply' microscopically 'bumpy'(?)... or
otherwise perhaps the newly formed singularities symmetrically merge
with the original in some way I can't guess at?

(Reminder: #7 is irrelevant if there was a 'no' answer somewhere along
the way)

First let me describe a simple case: a Schwarzschild black hole with an
infalling spherical shell of matter. Let the black hole have an
"effective mass" M, and the shell have a total mass m and radius R(t).
Initially the shell is far outside the horizon at r=2M, so for such
times one has the Schwarzschild solution for the region 2MrR(t) with
effective mass M, and one has a different Schwarzschild solution for the
region R(t)rinfinity with effective mass M+m. Birkhoff's theorem
implies both of these results, and the fact that the "kinetic energy of
infall" for the shell does not contribute (measure its mass m far from
the horizon while it has negligible "kinetic energy"). Note that R(t)
gets smaller with time, and as R(t)-2M, the shell approaches the
horizon. An observer between r=2M and r=2(M+m) will observe the horizon
to expand outward before the shell reaches her; the horizon expands with
local speed c. Both horizon and shell reach r=2(M+m) simultaneously.


andrew b wrote:
1: How will matter objects appear to distort as they indefinetly
approaches the horizon?

How distant objects "appear" to an observer depends on many different
things, and you have not specified enough:
a) how does the observer observe the distant object:
1) via a telescope
2) via assistants equipped with coordinate clocks and rulers
distributed throughout the region of interest so each
assistant reports the coordinates of a portion of the object
3) like (2) but with standard clocks and rulers
b) how does the object move:
1) is it in freefall
2) is it supported somehow and slowly approaching the horizon
3) is it accelerated towards the horizon
c) how does the object respond to tidal forces:
1) like a solid
2) like a liquid
3) like a gas
4) other
d) is the object:
1) small
2) large

If I select a2,b2,c1,d1 (which are the simplest set), then as the object
approaches the horizon (or, indeed, as it simply moves to smaller r),
its intermolecular bonds will maintain its PROPER shape, and since it
moves slowly we can ignore dt in the line element, so from the
Schwarzschild metric components it is clear that the assistants will
report that its transverse dimensions are unchanged (it is small), but
its radial COORDINATE size is decreasing. As this SMALL object
approaches the horizon, the assistants will report that it shrinks
radially without bound in COORDINATE size -- but those assistants will
require stronger and stronger rockets to maintain their and the object's
position, and the required proper acceleration also increases without bound.


If one selects a3,b2,c1,d1 the assistants will report no change in size
or shape. The assistants will of course still require stronger and
stronger rockets to lower the object SLOWLY toward the horizon.


2: Specifically, will they seem to in any way become flattened or
compressed (to an outsied observer)? (i.e. seeming to have less volume
for the same ammount of mass?) If the answer here is NO, then the
questions from 3 on are withdrawn.

3: If the answer to 2 was YES, then I would concluded that from all
external perspective the matter approaching an event horizon appears
to become denser. Now: what happens when the percieved density of some
part of the infalling matter is great enough that the external
observer would expect it to form another black hole, centered on the
infalling lump under question? Does another seperate (but
intersecting) event horizon come into being? (always, always from an
outside perspective)

Your questions are not sharp enough to have clear and definite answers.

But this I can say: all physics is LOCAL. So if the object itself (or an
observer collocated with it) observes its density to remain constant
(e.g. it acts as a solid and its intermolecular forces behave that way),
then it won't form a black hole no matter how large a distant or
relatively-moving observer may think its density is.

I can also say this: no horizon ever "comes into being" except as a
single point. Horizons can grow but never shrink. For a
spherically-collapsing star of mass M (a spherical mass exceeding the
Chandresekhar limit) at some instant while the surface is larger than
r=2M, a horizon forms at the center and starts expanding outward (with
local speed c); the horizon and surface reach r=2M simultaneously; the
horizon remains there but the surface keeps shrinking down to r=0.

And this: If one starts with a spherical black hole and drops a small
but massive object into it (i.e. small in size compared to r=2M but with
non-negligible mass), the horizon of the black hole will distort towards
the infalling object, and will envelope it before it reaches r=2M.
Following this the horizon will vibrate in complex ways, and
gravitational radiation will carry away all multipoles except its (new,
total) mass and its angular momentum.


4: If the answer to 3 is NO, another singularity does not form, then
is the following explanation for WHY one does not correct?: In an SR
situation, I believe, an object that is moving at a great relative
velocity to you will appear to become flattened, but yet (according to
the relativity.physics.faq, which I may or may not understand), it
will never appear to you as a black hole... Presumably despite the
fact that the object appears to you be compressed to a small enough
volume(?).

As I said, all physics is LOCAL. Note a fast-moving object is a QUITE
different physical situation than a mass approaching an event horizon.


5: If the explanation posed in #4 is CORRECT; in other words if the
situation of you observing an object very near a black hole is, in
fact, CONGRUENT to the SR situation of you observing a fast-moving
object IN THE CONTEXT THAT, despite the fact that the object would
appear to be very dense, it will never form a singularity, then I
think I understand what I want to understand... (to the limit of the
time when I can actually handle GR math and understand why the SR&GR
situations are congruent in this way)...

I dunno what you are trying to say. But I can see no way that the two
situations you described are "congruent" in any sensible way -- they are
quite different physical situations.


6: Just to confirm, then: an event horizon, once formed, can never
change in diameter? (again disregarding quantum effects)

Once formed, the area of an horizon can never decrease. It can increase
if one adds matter/energy.


7: If the SR and GR situations I've described are NOT congrous in that
approaching mass WILL compact to form a singularity... then I am
confused, because it would seem like an event horizon would slowly
accumulate many other event horizons 'sticking out of it' like
bubbles, and so on recursively(?);

The horizon can grow, but not split. Any bumps will get smoothed out
over time via gravitational radiation.


this is not something I have ever
heard discussed,

Look in:

K.Thorne, _Black_Holes_&_Time_Warps_.


Tom Roberts