Time, Gravity

[tomBitonti]

As above, that depends on the size of the hole. For smaller holes, yes, tidal forces would snap any material created by mortal hands. For larger holes, there is not notable tidal stress, period.

Well, I was considering the case where the mass of the chain is negligible, as compared to the object orbiting above, as I thought we were talking mostly about the relativistic time effects. If we're talking about something more notable, then that is an issue - you'll need to put energy into your upper orbital platform to keep it up there. But, honestly, that's true of an elevator around a normal planet, too - the arrangement is stable only to first approximation. In the real world, second-order and higher effects will mean the system requires upkeep.



Given that we've not yet observed any black hole well enough to know if it has spin or not, your guess is as good as mine. There's lots of models where the hole sheds the star's spin before final collapse, and others where it doesn't.

For the case of an anchor point in a stable orbit, and the lower point close to the event horizon, there seem to be large stresses which would be produced. For such an arrangement, the size of the black hole won't matter, will it, since the anchor is, say, at about 0.5c escape and the lower is slightly less than 1.0c?

Not sure what we can say about the distribution of black hole spins. Found this: http://www.bk.psu.edu/faculty/daly/D09a.pdf but haven't had time to read it.

Thx!

TomB

 

[freyar]

Funny, these threads always seem to pop up when I'm away from EN World on the weekend or busy at work or something. Anyway, as usual, Umbran has pretty much hit the nail on the head. However, I can add that, while direct observation of a black hole isn't possible, it is possible to infer the spin by looking at how closely stuff can orbit the black hole without falling directly in. The first case measured (known as GRS 1915+105), the spin was pretty much at the maximum value, so, just because the first one turns out that way, you'd think odds are that many astrophysical black holes do indeed spin fairly fast.

 

[Umbran]

For the case of an anchor point in a stable orbit, and the lower point close to the event horizon, there seem to be large stresses which would be produced. For such an arrangement, the size of the black hole won't matter, will it, since the anchor is, say, at about 0.5c escape and the lower is slightly less than 1.0c?

Here's the thing - the required escape velocity in and of itself is not telling us much. That only comes into play if you're trying to leave orbit, and then only if you're trying to leave ballistically. In trying to maintain an orbit, there will be two sources of strain on the cable - one is tidal, and that very much depends on the size of the hole. The other is in the force you need to keep the anchor from falling into the hole - this latter also will depend upon the size of the hold, and your distance from it's center (note, that's distance from the center, not from the event horizon).

 

[tomBitonti]

Here's the thing - the required escape velocity in and of itself is not telling us much. That only comes into play if you're trying to leave orbit, and then only if you're trying to leave ballistically. In trying to maintain an orbit, there will be two sources of strain on the cable - one is tidal, and that very much depends on the size of the hole. The other is in the force you need to keep the anchor from falling into the hole - this latter also will depend upon the size of the hold, and your distance from it's center (note, that's distance from the center, not from the event horizon).

Yes ... but, if the lower end is close to the event horizon, and the upper end is in a stable orbit, won't that force a certain amount of stress? The stress on a small body would depend on the size of the hole, as would the stress on the tether, but the stress on the tether depends also on the size of the tether, and that grows as the hole grows, if one end of the tether is close to the hole and on the other end is in a stable orbit (with stable orbits starting where the escape velocity is > 0.5c; the escape velocity at the event horizon is 1.0c.) I'm not sure how that all changes for a spinning hole, though, so maybe the inner radius of stable orbits changes for a spinning hole.

Thx!

TomB

 

[Umbran]

Yes ... but, if the lower end is close to the event horizon, and the upper end is in a stable orbit, won't that force a certain amount of stress?

As I just said - there are two basic sources of stress on the chain: 1) Tidal, and 2) the force required to hold up the anchor, as it isn't in a stable orbit. There isn't an extra "I'm near a black hole" stress.

Spinning black holes are interesting - but also complicated. Specifically, a spinning hole doesn't have just one event horizon you have to worry about. It has the usual spherical event horizon, which is surrounded by an oblate spheroid called an "ergosphere". If you have a real physical object in the ergosphere it *must* co-rotate with the hole (which, as has been noted, may be wicked damned fast). Put your anchor within the ergosphere, and either the chain snaps, or you get reeled in like a fish, to your doom.

So, really, leave the spinning holes out - you don't want to anchor to one.

 

[tomBitonti]

As I just said - there are two basic sources of stress on the chain: 1) Tidal, and 2) the force required to hold up the anchor, as it isn't in a stable orbit. There isn't an extra "I'm near a black hole" stress.

Will the tether experience a -- very large -- stress (without naming that stress as tidal or not) if one end is close to the event horizon, and the other is in a stable orbit?

Then, what do we call that stress? The two endpoints want to move in paths that don't maintain the shape of the body, and the "want to move" is due to the gravity of the black hole.

Thx!

TomB

 

[Umbran]

Will the tether experience a -- very large -- stress (without naming that stress as tidal or not) if one end is close to the event horizon, and the other is in a stable orbit?

As I've noted before, it depends upon the specifics. So let us look at them...

Let us assume the following: You have a ship in a stable orbit, and you drop an anchor. The anchor has a mass notably smaller than the ship, and the mass of the chain between them is outright negligible. The anchor is in a position where no stable orbit exists. All these objects are in free fall.

If the black hole is small enough, tidal forces will simply break the chain (or even "spagettify" the anchor). That's an uninteresting scenario. So, let us assume that the black hole is large enough that this isn't an issue - and we assume the tidal forces from the hole are not enough to destroy any of the items on their own.

This position is still fundamentally unstable. The anchor *will* pull the ship out of orbit, eventually. It may do this slowly, with no particularly major stress upon the chain, but eventually tugging the ship down, regardless. The "stable orbit" does not allow the ship to exert notable forces - it isn't a fixed point, like it is nailed down in the sky, or sitting in a groove that's hard to pull it out of, or something. It is just floating there, and will float around *only so long as you don't pull or push on it*, but the anchor is now pulling on it, so it is coming down. It doesn't take a huge pull, just a small pull over time will be sufficient.

So, you have to turn on the ship's engines - the ship is in powered flight, now. The maximum stress upon the chain is now capped by the ship's engines. Is this "very large"? Well that depends upon your ship.

 

[Bullgrit]

The thing that is kind of twisting my brain: the cable connecting the anchor and the orbiting spacecraft essentially stretches through time as much as it stretches through space between the two ends. One end is pretty much stuck at one point in time (the past), and the other end is continuing through the future. What happens if we send an astronaut down the cable? Does he go back in time the closer he gets to the anchor (which is stuck in the time when it was dropped)?

Bullgrit

 

[tomBitonti]

As I've noted before, it depends upon the specifics. So let us look at them...

Omitting a lot of details.

I don't think mass is an important detail (other than issues of the relative masses of the endpoints, if we use careful positioning to balance forces). All of the forces are proportional to the endpoint mass, as will be (roughly) the mass of the tether (given a fixed strength of tether). I'd expect mass to mostly factor out of the equations. A given is that the masses of the endpoints and the tether are small enough to be disregarded as to considerations of the gravitational field.

What I'm looking at is the necessary positioning of the endpoints and what that implies about the stress on the tether. If the lower endpoint is placed "close" to the event horizon and the upper endpoint is placed in a stable orbit. That puts a difference in field strength which corresponds to a difference of escape velocity of 0.5c. The difference will be higher if the upper endpoint is not close to being in a minimal stable orbit. Won't that cause a huge stress???

An additional issue, which I think is what you are getting at, is what to call the tether stress, and is it appropriate to think of that as being a "tidal" stress. A question here is whether we are talking about the curvature tensor measured close to the event horizon, or the force between two distant points which are prevented from moving in a geodesic, which (I'm thinking, but at the edge of my depth) will be related to an integral of the curvature tensor between the points.

Thx!

TomB

 

[tomBitonti]

The thing that is kind of twisting my brain: the cable connecting the anchor and the orbiting spacecraft essentially stretches through time as much as it stretches through space between the two ends. One end is pretty much stuck at one point in time (the past), and the other end is continuing through the future. What happens if we send an astronaut down the cable? Does he go back in time the closer he gets to the anchor (which is stuck in the time when it was dropped)?
Bullgrit

What sticks in my brain is a question of whether a point infalling to a black hole is considered to actually cross the event horizon. Won't any signals emitted by an infalling object be red-shifted to be as faint as the hawking radiation of the black hole? Can external observers model the history of the infalling object as a fall which is gradually turned into an outflow of hawking radiation?

Thx!

TomB