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space elevator near a black hole (mindwarping idea warning)

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FrodoGoofballCoTV from Colorado, USA Since: Jan, 2001
#1: Apr 21st 2011 at 4:28:51 PM

A space elevator is a hard(er) sci-fi idea that works something like this: you start off with an advanced civilization and a largish space station with heavy industrial equipment and some thousands of km of seemingly near - infinitely strong cable onboard. You move the space station into geosynchronous orbit and lower a capsule from the space station toward the planet on the line, adjusting the orbit and / or counterweights to keep the capsule over the same spot. You then attach the cable to the planet and build a giant elevator that can move moderately large cargoes into high orbit for less than the cost of using rockets, without ever reaching low altitude orbit speeds.

Now I was reading this again, and I got to thinking about the idea of a space station that was so large (light years in diameter) it was technically a black hole, even though the density was quite low by earthly standards (e.g., the average density within the event horizon is less than air at sea level), the surface gravity is less than Earth's, and tidal forces are near - negligable. If you had an infinitely strong cable, what if you built a space elevator that connected a point inside the event horizon to a point outside the event horizon? Under newtonian physics, you could use it to ascend through the event horizon at a speed slower than light to a point where sublight speeds would enable travel from the black hole.

Of course in Cloud Cuckooland this insanity might be plausable, but in mainstream hard Sci-Fi by definition if you can escape a black hole you have some pretty kick - ass FTL and therefore also time travel.

I was wondering what any of our resident relativity experts would say about this?

KnightofLsama Since: Sep, 2010
#2: Apr 22nd 2011 at 2:04:55 AM

Not trying to be rude (but not really trying to be polite either) but there are so many problems with this I scarcely no where to begin.

Problem 1) Black Holes DO NOT WORK THAT WAY!. You can make an object as large as you want, galaxy sized even but not matter how large you make it, it will never be 'so large it was technically a black hole'. Black holes are defined having all their mass collapsed into an infinitesimally small point. Also the really big ones like those that dwell at the heart of our galaxy, actually have quite low average densities anyway (in this case average density being defined as the mass divided by the volume enclosed by the event horizon).

Problem 2) Space Elevators and event horizons do not mix. For a space elevator to work the counterweight must be orbiting the main body of the system at the same rate as main body rotates. Spinning black holes produce a phenomenon known as frame dragging that twists the local space-time metric into knots. In some models, for particularly rapidly spinning black holes, the reference frame drag can actually exceed c. Even for less extreme cases no material even theorised cloud stand the stresses involved.

Problem 3) If you belong to a civilisation capable of building artificial structure with a size measured in light years you are so far up the Kardashev Scale, you don't need space elevators anymore.

Yej (4 Score & 7 Years Ago) Relationship Status: They can't hide forever. We've got satellites.
#3: Apr 22nd 2011 at 3:15:01 AM

(in this case average density being defined as the mass divided by the volume enclosed by the event horizon).
This is sort-of-constant, IIRC. The measurement of the event horizon radius scales depending on mass.

Also, the whole scenario falls apart for the very simple reason that Relativity does not permit a material strong enough, and Newtonian dynamics doesn't let you have a black hole in the first place.

KnightofLsama Since: Sep, 2010
#4: Apr 22nd 2011 at 5:20:00 PM

This is sort-of-constant, IIRC. The measurement of the event horizon radius scales depending on mass.

Yes, radius scales linearly with mass. But volume scales to the radius cubed. A black hole of one solar mass is going to have an event horizon of radius R enclosing a volume V but a black hole of two solar masses is going to have an event horizon radius of 2R enclosing a volume of 8V which means its average density is only going to be a quarter of a one solar mass black hole.

Yej (4 Score & 7 Years Ago) Relationship Status: They can't hide forever. We've got satellites.
#5: Apr 23rd 2011 at 4:40:27 AM

Yeah, but the density of a black hole doesn't affect that much. It's the proto-black-hole mush's density you need to worry about.

KnightofLsama Since: Sep, 2010
#6: Apr 23rd 2011 at 5:13:57 PM

[up] True enough. I originally brought it up with respect to the OP's comment about low density to point out that black holes can have a low average density quite naturally.

JHM Apparition in the Woods from Niemandswasser Since: Aug, 2010 Relationship Status: Hounds of love are hunting
Apparition in the Woods
#7: Apr 24th 2011 at 4:58:06 AM

I think that the ship being a black hole is almost less of a problem than the tensile strength of the material implied. Seriously, something that could survive that level of gravitational pull—not "space station-level," but "black hole/strange star-level"—would basically have to be made of black hole material in-and-of-itself... Which is basically magic.

Sorry, but unless your civilisation is mind-shatteringly advanced, this isn't going to happen.

On a related note: I feel that it would be relevant to point out something about quantum critical shells *

here, but I'm not sure why.

Oh, wait....

Your rope would basically be made of them. I don't know how that would work. I don't know if anyone knows how that would work.

edited 24th Apr '11 5:00:45 AM by JHM

I'll hide your name inside a word and paint your eyes with false perception.
Yej (4 Score & 7 Years Ago) Relationship Status: They can't hide forever. We've got satellites.
#8: Apr 24th 2011 at 5:03:02 AM

It doesn't. Relativity does not permit any material capable of crossing the event horizon and remaining in one peice.

JHM Apparition in the Woods from Niemandswasser Since: Aug, 2010 Relationship Status: Hounds of love are hunting
Apparition in the Woods
#9: Apr 24th 2011 at 10:38:41 AM

My point exactly. To our current knowledge and technology, it is functionally impossible.

By the way: I don't like saying that any thing is just impossible. It may well be theoretically possible, somehow; we just have no reasonable, sane idea how that doesn't involve Failing Physics Forever.

Or, you know, Cthulhu.

edited 24th Apr '11 10:39:28 AM by JHM

I'll hide your name inside a word and paint your eyes with false perception.
Yej (4 Score & 7 Years Ago) Relationship Status: They can't hide forever. We've got satellites.
#10: Apr 24th 2011 at 1:06:29 PM

Even theoretically, it is completely impossible. This is because at the event horizon, the numbers that control the geometry of spacetime get flipped around. Space becomes time, with the black hole singularity suddenly occupying the position of "later". Anything inside the horizon cannot avoid falling into the black hole, just as nothing can avoid progressing to tomorrow.

Additionally, the event horizon marks the point where the velocity you'd need to escape that sphere is c. In order for a material to actually remain joined up into a macroscopic thing, some force must keep it together. (Usually electromagnetism, but atoms are kept together by the strong force.) No force can propagate faster than c, and so no force escapes the black hole's horizon. Thus, your material, no matter what it's made of, falls apart.

edited 24th Apr '11 1:07:33 PM by Yej

JHM Apparition in the Woods from Niemandswasser Since: Aug, 2010 Relationship Status: Hounds of love are hunting
Apparition in the Woods
#11: Apr 24th 2011 at 1:25:22 PM

You're kind of missing my point. In the next couple thousand years or so, who knows what weird exceptions to our currently held laws of physics we might find? But, as I said: Trying to speculate on what those exceptions might be is quintessentially futile.

In other words: According to the laws of nature and the universe as we currently understand them, stringing together tiny black holes into a rope is preposterous. As we might later understand them... It will probably still be preposterous, but who knows?

This is why language-oriented people should not engage in science-oriented discourse without a translator...

I'll hide your name inside a word and paint your eyes with false perception.
tracer Since: May, 2009
#12: May 8th 2011 at 12:50:29 PM

How big would a ball of solid iron have to be before its own Schwarzchild Radius became larger than itself?

FrodoGoofballCoTV from Colorado, USA Since: Jan, 2001
#13: May 8th 2011 at 8:28:47 PM

Problem statement:

Algebraic solution

  • d = m/((4/3)*pi*r^3) = 3*m/4*pi*r^3; 3*m = 4*pi*d*r^3; m = (4/3)*pi*r^3*d
  • r = (2G/c^2) * ((4/3)*pi*r^3*d) = (4*2*pi*G*r^3*d)/(3*c^2); r/r^3 = (4*2*pi*G*d)/(3*c^2) = r^-2 = ((8*pi*G)/(3*(c^2)))*d
  • r^2 = ((3*(c^2))/(8*pi*G)*d); r = sqrt (((3*(c^2))/(8*pi*G)*d)) = (c/2) * sqrt (3/(2*pi*G)) * sqrt (1/d)

Numeric solution

Tl;dr:

  • 286 million km in diameter; the mass would be ~48 million solar masses.

Note that an iron sphere which we kept adding mass to (at constant density) would likely collapse into a black hole long before it reached that size due to mechanical failure of the atomic electron shells.

The same calculation for:

  • density of water => 800 million km dia, 136 million solar masses.
  • density of air at sea level => 22.9 billion km dia (larger than the orbit of Pluto), 3.9 billion solar masses.

edited 8th May '11 11:36:28 PM by FrodoGoofballCoTV

Yej (4 Score & 7 Years Ago) Relationship Status: They can't hide forever. We've got satellites.
#14: May 9th 2011 at 9:24:39 AM

That seems unreasonably high, since you can get black holes made of hydrogen out of only a few hundred, at most, solar masses.

FrodoGoofballCoTV from Colorado, USA Since: Jan, 2001
#15: May 9th 2011 at 10:40:43 AM

[up]Well, theoretically, you can make a black hole out of <1 solar mass of hydrogen if you compress it enough.

I'm just talking about making a black hole without allowing the gravity to collapse the structure (i.e., keeping denstities constant and increasing volume until an event horizon begins to form).

Obviously in real life, using only "normal" matter, this would not be a phenomena that would plausably occur.

edited 9th May '11 10:40:54 AM by FrodoGoofballCoTV

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