Darren New <dne### [at] sanrrcom> wrote:
> Saying we're not inside a black hole implies we know what happens inside 
> a black hole.

  If we were inside a black hole, GR would be wrong, because GR predicts
certain things about the inside of a black hole (such as all space-time
geodesics going to the singularity), and this is clearly not the case
in our observable universe.

  Given that it's GR which predicts the existence of black holes, and
saying that we may be inside a black hole, which means that GR doesn't
apply after all, it would be a statement that defeats itself: If GR doesn't
apply, then how can be was we are inside a black hole, which is a consequence
of GR?

> Plus, a sufficiently large black hole can have a 
> surprising amount of livable space inside.

  But according to the GR equations everything inside the event horizon
of the black hole would inevitably crunch into the singularity. There's
no avoiding it. Inside the event horizon moving in time is equivalent to
moving in space, and all the timelines go to the singularity. Even if a
force was applied to an object to try to keep it away from the singularity
it wouldn't help, because the object travels in time.

  Source:
http://en.wikipedia.org/wiki/Schwarzschild_metric#Singularities_and_black_holes

  Basically what you are saying is that GR applies inside the event
horizon as if there was no event horizon and no singularity, which is,
of course, contradictory.

  Of course this is how I understand it. I wouldn't be surprised if I'm
wrong. There are many features of GR which I have had and still have
difficulties in understanding (the most recent case being the concept of
the cosmological horizon, which to me seemed impossible at first).

> How do you know everything doesn't go to a singularity in the future? 
> That would be the "big crunch" theory, which I understand scientists 
> believe is true if the universe contains enough mass to be finite in size.

  If all geodesics and timelines point towards the singularity, how can
anything go away from the singularity?

  Anyways, the current consensus, based on measurements, seems to be that
the universe is not only expanding, but is doing so at an accelerated rate.
It seems that there will not be a big crunch. The big rip seems more likely.

-- 
                                                          - Warp

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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> >   As far as I know, the universe is *expanding*, not going towards a single
> > point.

> If there's enough mass, then eventually gravity will pull everything 
> into a "single point", just like everything came from a single point 
> during the big bang. (At least, that's my lay understanding.)

  Even if that was so, it still doesn't mean we are inside a black hole.

  Anyways, it seems that this is not so after all.

> >   A star is not a black hole even during its own collapse. Not until it
> > gets inside its own Schwarzschild radius. Collapse does not mean that
> > the thing which collapses is a black hole.

> I'm not sure "Schwarzschild radius" makes sense in the context of "all 
> of space-time".

  Why not? The Schwarzschild radius of a given mass is simply a distance
which is the product of the mass and a constant. The Schwarzschild radius
of the universe is the mass of the universe times a that constant.

  If all the mass of the universe was compressed inside a volume smaller
than a sphere with that radius, it would form a black hole.

>  I.e., what does "radius of the universe" mean?

  It's not the "radius of the universe". It's the Schwarzschild radius.
Different thing.

-- 
                                                          - Warp

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Darren New <dne### [at] sanrrcom> wrote:
> >   It's true that nobody dares to even guess what is happening inside the
> > event horizon of a black hole. 

> Not true. They just won't guess what happens at the singularity. It's 
> called a singularity because the math breaks down there.

  No, I think it's inside the event horizon. While GR equations tell us
what happens if GR holds inside the event horizon in the same way as
outside it, it's still speculation.

> Calculate the gravitational curvature at the Schwartzchild radius for a 
> galaxy-sized black hole. It's not that great. You likely wouldn't even 
> notice you'd crossed any sort of boundary. (At least, that's what I've 
> read. I am not sure how to do the math myself.)

  I think you could clearly see the event horizon regardless of its size
because of the way it bends light.

  Once inside, you are doomed. There's no escaping the singularity.
You'll go there no matter what you do.

>  > However, if GR is right, everything inside
> > the event horizon inevitably goes to the singularity and there just isn't
> > escaping it. You just can't keep away from it no matter what you try.

> Sure. Let me know when you figure out how to escape the universe. :-)

  Nothing is going towards a global singularity in the universe. On the
contrary, everything is going away from everything else.

> >> Surely you're not asking seriously? A sphere is a 2D finite surface with 
> >> no border.
> > 
> >   The sphere is its own border.

> No, the sphere is a border for a ball, not a sphere.

  A ball is a sphere.

  Perhaps you are confusing it with a spherical surface?

-- 
                                                          - Warp

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Warp wrote:
>   Of course this is how I understand it.

You probably understand it somewhat better than I do. :-)

>   If all geodesics and timelines point towards the singularity, how can
> anything go away from the singularity?

But if it's a closed system that's (say) the 4D equivalent to the 
surface of a sphere, all geodesics *do* point towards the singularity, 
given enough time. I think.

>   Anyways, the current consensus, based on measurements, seems to be that
> the universe is not only expanding, but is doing so at an accelerated rate.

Yep. I wouldn't be surprised if this changes again, tho. :-)

-- 
   Darren New / San Diego, CA, USA (PST)
     It's not feature creep if you put it
     at the end and adjust the release date.

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Warp wrote:
>   Why not? The Schwarzschild radius of a given mass is simply a distance
> which is the product of the mass and a constant.

What's the distance from the universe?  Doesn't a distance have to be 
between two events?

>   If all the mass of the universe was compressed inside a volume smaller
> than a sphere with that radius, it would form a black hole.
> 
>>  I.e., what does "radius of the universe" mean?
> 
>   It's not the "radius of the universe". It's the Schwarzschild radius.
> Different thing.

How do you measure the "center" from which you take the radius of the 
sphere? I.e., "distance" implies two space-time events between which 
you're measuring a distance.

Certainly with enough mass, a finite universe *could* be within its 
Schwartzchild radius. But I don't think I know enough about this to 
really make any factual statements beyond that. :-)

-- 
   Darren New / San Diego, CA, USA (PST)
     It's not feature creep if you put it
     at the end and adjust the release date.

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Warp wrote:
>> Not true. They just won't guess what happens at the singularity. It's 
>> called a singularity because the math breaks down there.
> 
>   No, I think it's inside the event horizon. While GR equations tell us
> what happens if GR holds inside the event horizon in the same way as
> outside it, it's still speculation.

Fair enough. Altho people have spoken of time travel via rotating black 
holes and such, but I suppose that's speculation until someone finds one 
for sure. :-)

>   I think you could clearly see the event horizon regardless of its size
> because of the way it bends light.

Yes, but all mass bends light. Even "dark matter". :-)  It's kind of the 
GR definition of "mass".

>   Once inside, you are doomed. There's no escaping the singularity.
> You'll go there no matter what you do.

Yep. Big Crunch. :-) I think the math for charged rotating black holes, 
or those taking into consideration quantum effects, are less obvious.

>>  > However, if GR is right, everything inside
>>> the event horizon inevitably goes to the singularity and there just isn't
>>> escaping it. You just can't keep away from it no matter what you try.
> 
>> Sure. Let me know when you figure out how to escape the universe. :-)
> 
>   Nothing is going towards a global singularity in the universe. On the
> contrary, everything is going away from everything else.

At the moment, yes.

>>>> Surely you're not asking seriously? A sphere is a 2D finite surface with 
>>>> no border.
>>>   The sphere is its own border.
> 
>> No, the sphere is a border for a ball, not a sphere.
> 
>   A ball is a sphere.

Mathematically speaking, when mathematicians distinguish "sphere" from 
"ball", the latter includes the points at distance < radius, while the 
former includes only points at distance = radius.

http://mathworld.wolfram.com/Ball.html

(Occasionally I surprise myself with the useless information that sticks 
in my head. Last week it was the reproductive cycle of jellyfish.)

The reason I made the distinction was to imply that the surface of a 
sphere would be unbounded (as in, without any boundaries) to an entity 
restricted to the surface. Sure, you couldn't change your radius, but 
that's by definition of it being restricted to a sphere. An entity in a 
ball, on the other hand, can move outwards from the center and hit a 
boundary at the radius.

I believe Aristotle had an interesting insight (right or wrong). If 
there is a boundary to the universe, and you throw a rock at the 
boundary, what stops the rock? There can't be anything outside the 
boundary to stop the rock.

>   Perhaps you are confusing it with a spherical surface?


-- 
   Darren New / San Diego, CA, USA (PST)
     It's not feature creep if you put it
     at the end and adjust the release date.

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In article <477a9e54$1@news.povray.org>, dne### [at] sanrrcom says...
> Warp wrote:
> >   As far as I know, the universe is *expanding*, not going towards a si
ngle
> > point.
> 
> If there's enough mass, then eventually gravity will pull everything 
> into a "single point", just like everything came from a single point 
> during the big bang. (At least, that's my lay understanding.)
> 
Actually, one aspect of at least one multi-universe system implies that 
the big bang may have been a "white hole". Which is to say, something 
that spews out matter, rather than condensing it. The math implies that 
nearly any such structure though is unstable. I.e., it will only spew 
matter for a short duration, from a singularity, before it stops doing 
so. The question then becomes, "Did the white hole generate enough 
matter, and with it, other forces, to prevent the whole thing falling 
into a singularity again?" However, you are talking about GR. Quantum 
mechanics, which GR doesn't apply to so well, implies that at the level 
of a singularity its impossible to everything to fall into one, without 
something getting back out again at all (i.e. Hawking's Radiation). Even 
nastier is the implication that the structure of what comes out is 
derivative of the material that goes in, such that information is never 
lost in the system. Prior assumptions implied that the structure of a 
thing, once in a black hole, would be randomized, such that it would 
never come out in a mathematically predictable form.

-- 
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    if version = "Vista" {
      call slow_by_half();
      call DRM_everything();
    }
    call functional_code();
  }
  else
    call crash_windows();
}

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Darren New <dne### [at] sanrrcom> wrote:
> >   If all geodesics and timelines point towards the singularity, how can
> > anything go away from the singularity?

> But if it's a closed system that's (say) the 4D equivalent to the 
> surface of a sphere, all geodesics *do* point towards the singularity, 
> given enough time. I think.

  I must admit that I have no idea what the GR equations say about this,
but I got the impression that inside the event horizon all geodesics point
straight at the singularity, when going forward in time. I would expect
that no geodesic points away from the singularity at any point.

-- 
                                                          - Warp

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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> >> Not true. They just won't guess what happens at the singularity. It's 
> >> called a singularity because the math breaks down there.
> > 
> >   No, I think it's inside the event horizon. While GR equations tell us
> > what happens if GR holds inside the event horizon in the same way as
> > outside it, it's still speculation.

> Fair enough. Altho people have spoken of time travel via rotating black 
> holes and such, but I suppose that's speculation until someone finds one 
> for sure. :-)

  I think the time travel is related to wormholes. Travelling inside a
wormhole does not imply going inside the event horizon of a black hole.

> >   I think you could clearly see the event horizon regardless of its size
> > because of the way it bends light.

> Yes, but all mass bends light. Even "dark matter". :-)  It's kind of the 
> GR definition of "mass".

  I said "they way it bends light", not "because it bends light".

  No mass is dense enough to bend light like a black hole does because,
obviously, if the mass was dense enough, it would collapse into a black
hole...

> >   Once inside, you are doomed. There's no escaping the singularity.
> > You'll go there no matter what you do.

> Yep. Big Crunch. :-)

  I think the analogy is not correct.

  The Big Crunch means that the universe, ie. space itself, contracts
until everything collapses into a singularity. Contraction of space doesn't
involve objects moving. (This is one of the hardest things to understand
about the expansion (and theoretical contraction) of the universe. One
counterintuitive result of the expansion of the universe is that the
distance between two objects can grow faster than c, which at first sounds
like it would break GR, but this is not so.)

  A black hole doesn't contract. Instead, objects physically move towards
the singularity.

> >   Nothing is going towards a global singularity in the universe. On the
> > contrary, everything is going away from everything else.

> At the moment, yes.

  I can't say for sure, but I have the understanding that anything going
away from the singularity inside the event horizon of a black hole would
be against GR equations.

> (Occasionally I surprise myself with the useless information that sticks 
> in my head. Last week it was the reproductive cycle of jellyfish.)

  Whatever floats your boat. ;)

-- 
                                                          - Warp

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Warp wrote:
>   I must admit that I have no idea what the GR equations say about this,
> but I got the impression that inside the event horizon all geodesics point
> straight at the singularity, when going forward in time.

I wouldn't think they point *straight* at the singularity, unless a 
photon spiraling to its death is considered to be going in a "straight" 
line. The fact that two particles can take different paths starting from 
the same place would seem to imply that "straight at the singularity" is 
either mistaken or so counter-intuitive that I don't understand what it 
means. :-)

Take a photon that's halfway to the S-radius (for some meaning of 
"halfway"). Fire it perpendicular to the radius (for some meaning of 
"perpendicular"). I would think the photon would follow a spiraling 
descent, rather than fall straight towards the singularity. Fire one in 
the opposite direction. It'll take a different path. If photons always 
follow geodesics, either you can have multiple geodesics pointing 
"straight at" the singularity, or your impression is wrong. I don't know 
which it would be, tho.

> I would expect
> that no geodesic points away from the singularity at any point.

Yeah. I'm just not sure the math works the same when you consider the 
whole universe to be the black hole. If it were true, how could you 
measure the "center" of the black hole? *I* sure don't understand the 
subject well enough to be sure. I'm just saying what I've heard other 
reputable GR scientists say.

Fun to babble about it, tho. ;-)

-- 
   Darren New / San Diego, CA, USA (PST)
     It's not feature creep if you put it
     at the end and adjust the release date.

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