"clipka" <nomail@nomail> wrote:
> So from this, and hearing that it would actually take an eternity (as seen from
> an outside observer) to *reach* the event horizon, it sounds logical to me that
> in fact the event horizon *is* the singularity...

Again, from the book since I probably can't state it any better:

"In this case, we will find that while the surface r=2m has some unusual
properties, the singularity is due to the choice of coordinates, and so is a
*coordinate singularity*.  Simply put, by using a different set of coordinates
we can write the metric in such a way that the singularity at r=2m is removed.
However, we will see that the point r=0 is due to infinite curvature and cannot
be removed by a change in the coordinates."

I may be guilty of having implied that the curvature is infinite at the event
horizon, but it looks like only the redshift to an outside observer is.  Kinda
learning this as I go, so you'll have to forgive me.

I know most of this is focused on general relativity, but here's a nifty program
for exploring special relativity:

http://realtimerelativity.org/

 - Ricky

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triple_r wrote:
> I may be guilty of having implied that the curvature is infinite at the event
> horizon, but it looks like only the redshift to an outside observer is.  Kinda
> learning this as I go, so you'll have to forgive me.

Ha! You're teaching me as you go! :-)

-- 
   Darren New, San Diego CA, USA (PST)
   "Ouch ouch ouch!"
   "What's wrong? Noodles too hot?"
   "No, I have Chopstick Tunnel Syndrome."

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Darren New <dne### [at] sanrrcom> wrote:
> You give one particle that is constantly emitting photons in all directions
> a push due south towards the singularity. You have an observer due north of
> the singularity looking south.  The observer due north will continue to see
> photons coming off the particle indefinitely?

Yes - they'll just seem to come at ever longer intervals (and with an ever
stronger redshift).

Of course, there is only a limited number of photons the particle can emit
before hitting the EH. However, from the observer's point of view, the very
last such photon will arrive at (roughly) infinite time after the second to
last.

Roughly, if that last photon is emitted a finite time before the particle passes
the EH.

Exactly, if the last photon is emitted at the very moment the particle passes
the EH.


>
> > it sounds logical to me that
> > in fact the event horizon *is* the singularity...
>
> But it's not.

Sure? Were you there and had a look? Do you grok the formulae? I don't ;)

>
> > If you'd take that trip, you'd experience it as being torn to
> > pieces by tidal forces,
>
> Tidal forces are a difference in gravity gradient between head and feet.
> It's not an absolute number. A sufficiently small pebble would experience
> very little tidal effect regardless of how close to the primary it orbits. :-

No, tidal forces are a difference in gravitational *force* - which (possibly
very simply speaking, as I'm not perfectly familiar with the terms) *is* the
gravity gradient. And they don't jsut rip apart your head and feet

If it was just your feet being pulled away from your head, you would be torn in
two because the force would pull on the whole chain of electromagnetic forces
tying your feet to your head, and some "weakest link" will give way.

This is not the case for tidal forces due to a gravity gradient: These will pull
on each link in the chain of electromagnetic forces separately - each link
subject to its own little gradient.

This will allow you to sustain a lot more gradient between your head and your
feet, possibly even without much adverse effect. But when it will ultimately
rip the skin off your feet, it will just as well rip apart the grains of sand
in your shoes.

Oh, and BTW, once you hit the EH, I guess there'll probably be no floating
around... with so much mass in so little space, there'll probably be not enough
room to swing a cat...

.... but then again, that place may be quite crowded already even outside the EH.

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Darren New <dne### [at] sanrrcom> wrote:
> Ha! You're teaching me as you go! :-)

If it helps, I'm trying to be pretty conservative in the insight I offer.  Hey -
it could be worse.  I could have written a book on the subject like this guy
did.  Now he probably knows and understands exactly what he's doing, but there
are errors left and right.  I followed the derivation, then plotted the
equations.  Then plotted them again.  And again.  Then derived it myself and
figured out that, indeed, he had a blatant sign error (one of many
errors/typos).  Perhaps I should have waited for the second edition.  Anyway,
didn't your mom tell you not to trust newsgroup physics debates?

 - Ricky

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Darren New <dne### [at] sanrrcom> wrote:
> Darren New wrote:
> >> it sounds logical to me that
> >> in fact the event horizon *is* the singularity...
> >
> > But it's not.
>
> By which I mean:
>   "singularity" has a specific meaning in mathematics, and the event horizon
> doesn't meet that definition, while the "center" of the black hole does.
>
> Take the graph of tan(x). At pi/2, there's a singularity. At 0, it just goes
> thru a 45-degree slope (and a point of inflection). That's kind of the
> difference.

Well, from an outsider's perspective - given that everything falling into the
black hole comes to a standstill at the EH... doesn't this qualify for a
singularity?

Okay, granted, from the poor victim's POV the singularity is still a few yards
away...


BTW, I've looked at the illustration with the "bent" ray by now, and the
illustration of what somebody falling into a black hole would see, and am now
coming to yet another conclusion:

I think that as a person closes in to the event horizon, (a) from his
perspective the *universe* will begin to collapse to a singularity (although
not a point, but rather a line), and (b) the event horizon will appear to
recede - until he hits the singularity, which in this sense is again identical
to the event horizon.

What happens then? Well - I guess that poor sod just falls through.
Back into the universe - which by then has aged by an infinite amount of time.
The only thing the poor guy suffered will be that he'll be turned around by 180
degrees when emerging from the singularity...

From an observer's point of view, the guy should thus appear at the other side
of the EH (and again take infinite time to get out of it).


You remember the famous greek thought experiment about Achilleus trying to catch
up with a turtle, and being unable to - because whenever he reaches the point
where the turtle was, the turtle will have crawled yet another bit ahead?

I guess we have a similar paradoxon here: An outside observer will see things
from the greek philosophers' point of view, in which a person heading for the
EH will never reach it. The poor victim, however, sees things from the classic
everyday perspective we know: He can just run past the turtle, no problem.

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Darren New <dne### [at] sanrrcom> wrote:
> It's possible I got that wrong.  Indeed, it's possible I don't know anything
> at all about the subject that I think I do. :-)  Were this an actual
> scientific forum, I'd have shut up a long time ago.

Well, same with me - but that's the fun part about it: Nobody *expects* us to
know what we're talking about, so we can let our imagination run wild ;)

> > AIUI the cosmological horizon is just the distance we can see *now*. Everything
> > beyond will become visible to us over time. Theoretically speaking.
>
> Oh, the event horizon. No, I think it's caused by space itself expanding,
> due to the big bang sort of thing.  If it all collapses again, that's a
> different question.

But if it all collapses again, then we couldn't have such an event horizon,
right? After all, it would all "boil down" (literally ;)) to a single point
again, where all the stuff will be able to interact once more...

(Then again, currently scientists claim we'll all be ripped to pieces one day by
the ever-faster expanding space within us all... hmmm... "the space within us" -
sounds a bit hippie-ish ;)

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triple_r wrote:
> didn't your mom tell you not to trust newsgroup physics debates?

Definitely.  I'll try not to fall into any singularities before checking 
with an actual knowledgeable physicist. :-)

-- 
   Darren New, San Diego CA, USA (PST)
   "Ouch ouch ouch!"
   "What's wrong? Noodles too hot?"
   "No, I have Chopstick Tunnel Syndrome."

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"triple_r" <nomail@nomail> wrote:
> "In this case, we will find that while the surface r=2m has some unusual
> properties, the singularity is due to the choice of coordinates, and so is a
> *coordinate singularity*.  Simply put, by using a different set of coordinates
> we can write the metric in such a way that the singularity at r=2m is removed.
> However, we will see that the point r=0 is due to infinite curvature and cannot
> be removed by a change in the coordinates."

Hm... yeah, maybe that's a mathematical way to describe what I'm currently
pondering: If we choose the falling victim's co-ordinates (location, time,
speed and all) a reference frame instead of that of a "fixed" outside observer,
we move the singularity from r=2m towards r=0 - from the Schwartzschild-Radius
(the "classic" EH) towards the "classic" singularity...

So I'd say the EH is the projection of the singularity into the reference frame
of an observer...

> I may be guilty of having implied that the curvature is infinite at the event
> horizon, but it looks like only the redshift to an outside observer is.  Kinda
> learning this as I go, so you'll have to forgive me.

Not a problem at all - as it seems, we're all in that same boat here ;)

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clipka escreveu:
> Darren New <dne### [at] sanrrcom> wrote:
> I think that as a person closes in to the event horizon, (a) from his
> perspective the *universe* will begin to collapse to a singularity (although
> not a point, but rather a line), and (b) the event horizon will appear to
> recede - until he hits the singularity, which in this sense is again identical
> to the event horizon.

Will he or any matter draw into the blackhole ever hit the singularity? 
  Does the singularity or blackholes even exist or are merely the point 
where GR equations break?

We're doing no better than ancient philosophers trying to split the 
matter and thinking about its outcome without a shred of evidence or 
measurements... which is the point of the GM guy in the article this 
thread links to:

"We start with effects actually seen in the lab, which I think gives it 
more credibility than black holes"

evidence.

> What happens then? Well - I guess that poor sod just falls through.
> Back into the universe - which by then has aged by an infinite amount of time.
> The only thing the poor guy suffered will be that he'll be turned around by 180
> degrees when emerging from the singularity...
> 
> From an observer's point of view, the guy should thus appear at the other side
> of the EH (and again take infinite time to get out of it).

If we assume blackholes exist, without much evidence so far, how about 
going even further in the imagination?  What if our 4D space-time isn't 
but a section of higher dimensional spaces, like a julia fractal section 
rendered in povray?  Perhaps the blackhole is then just a curve along 
this surface and the poor fellow ends up in another region of 
space-time.  The original outside observer will never see him again, 
unless he goes all the way back through the worm hole...

> You remember the famous greek thought experiment about Achilleus trying to catch
> up with a turtle, and being unable to - because whenever he reaches the point
> where the turtle was, the turtle will have crawled yet another bit ahead?
> 
> I guess we have a similar paradoxon here: An outside observer will see things
> from the greek philosophers' point of view, in which a person heading for the
> EH will never reach it. The poor victim, however, sees things from the classic
> everyday perspective we know: He can just run past the turtle, no problem.

Those greeks philosophers were just full of marijuana.  And pasta.  They 
were first possibly the first thinkers of mankind to think too much on 
far too abstract subjects rather than more mundane and practical 
matters... :P

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clipka escreveu:
> Darren New <dne### [at] sanrrcom> wrote:
>> It's possible I got that wrong.  Indeed, it's possible I don't know anything
>> at all about the subject that I think I do. :-)  Were this an actual
>> scientific forum, I'd have shut up a long time ago.
> 
> Well, same with me - but that's the fun part about it: Nobody *expects* us to
> know what we're talking about, so we can let our imagination run wild ;)

Don't worry, you guys!  Even scientists let their imaginations run wild 
too...

This was a very interesting thread, despite being a very difficult and 
misunderstood subject among laymen.  But I'm actually amazed by how few 
were drawn to it.  I thought most geeks love space talk and povray is 
full of geeks after all! :D

>>> AIUI the cosmological horizon is just the distance we can see *now*. Everything
>>> beyond will become visible to us over time. Theoretically speaking.
>> Oh, the event horizon. No, I think it's caused by space itself expanding,
>> due to the big bang sort of thing.  If it all collapses again, that's a
>> different question.
> 
> But if it all collapses again, then we couldn't have such an event horizon,
> right? After all, it would all "boil down" (literally ;)) to a single point
> again, where all the stuff will be able to interact once more...

Since we're speculating, if space is really expanding, do you think in 
absolute terms we're now much larger than dinosaurs back in their day? 
Of course, fossils won't tell, cause they expanded ever since too. ;)

> (Then again, currently scientists claim we'll all be ripped to pieces one day by
> the ever-faster expanding space within us all... hmmm... "the space within us" -
> sounds a bit hippie-ish ;)

I don't want to live to see proton decay!  well, not that I would 
anyway... :P

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