Time, Gravity

[Bullgrit]

Reading about the space elevator concept got me thinking about this. It is known that time is slower near Earth's surface, and faster out in space. Plus, the faster one moves, the slower time moves. So with a space elevator -- anything that has a physical link from Earth's surface to an "anchor" in space -- the space anchor would be in a faster time than the Earth base. And along the physical link, time would be different along each measurable piece.

Dropping an anchor from an orbiting spacecraft into a black hole, the anchor going down would be slowing in time. What would be the effects of this? Once the anchor reaches a close proximity to the event horizon, it would be almost stopped in time, but the orbiting spacecraft would still be moving around. What's the theoretical outcome of this?

Bullgrit

 

[Fiddleback]

Without diving into the actual physics of the thing, I think the biggest obstacle to your idea is that, while a Space Elevator would be going faster at it's top than at it's bottom (Much like a record has to go faster at the outer edge than in the center) the over all gain in speed, while impressive to us mere mortals, is absolute peanuts when compared to the speed of light itself.

Thus, any time difference would be on such a small scale as to make no real difference at all.

As for anchors down black holes... (I'm about to get this possibly very wrong, so forgive me if I do) I think you have to treat the anchor as being part of the system to which it is attached. In other words, you aren't just dropping the anchor, but the anchor, it's chain and the ship to which it is attached as one whole unit. I believe that when the anchor enters the event horizon you have to consider that the whole system has therefore entered the event horizon.

That is my, non-refundable and entirely overvalued, two cents.

 

[Fiddleback]

Sorry, one more thing. The 'time is faster out in space' bit depends on where the observer is observing from.

 

[tomBitonti]

You wouldn't be able to maintain a tether so close to a black hole. Tidal forces would smash it apart.

But, using a black hole really complicates the physics. The physics are rather complicated by the spin and charge of the black hole, and because you can't use linear approximations any more.

This seems to be a decent link: http://users.wpi.edu/~paravind/Publications/PKASpace Elevators.pdf

Lots of other links out there to be found. This one talks specifically about satellites and time differences:

http://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Relativity

Mostly, the effects that are there will be due to the position of an observer in the gravity well and the velocity of the observer, with usual transformations between the frames of reference. I don't think there is anything much exceptional: Time dilation due to frame differences. Stresses on the tether because they are probably preventing at least one endpoint from following a geodesic. If you sent a signal between endpoints, it would want to follow a slightly different path than the tether (unless you managed the geometry very carefully).

TomB

 

[Umbran]

As for anchors down black holes... (I'm about to get this possibly very wrong, so forgive me if I do) I think you have to treat the anchor as being part of the system to which it is attached. In other words, you aren't just dropping the anchor, but the anchor, it's chain and the ship to which it is attached as one whole unit. I believe that when the anchor enters the event horizon you have to consider that the whole system has therefore entered the event horizon.

Nope. Not in the least.

What happens is rather like.. a ship dropping its anchor! I mean, really. Think of a real ship - forget the black hole. It drops an anchor, and that sticks it mostly in place. If the ship tries to move around a lot while the anchor is down, the ship may be damaged. But, the ship is still up at the surface, and the anchor is still at the bottom of the sea.

As the anchor approaches the black hole, it will become harder and harder to draw it back up. You could orbit around the hole - there's no resistance to movement parallel to the surface of the event horizon - but the closer the anchor gets to the event horizon, the more energy you'd need to pull it back up. If you let the anchor actually enter the event horizon, well, you're never getting it back. You are now tethered to that black hole for all eternity. Not that any chain in existence is likely to be able to withstand the stresses involved. It'd probably jut snap somewhere along its length, or rip out of its mooring on the ship.

 

[Umbran]

But, using a black hole really complicates the physics. The physics are rather complicated by the spin and charge of the black hole, and because you can't use linear approximations any more.

If it has such. In the business, when you're talking to non-specialists and say, "A black hole", we generally assume one that has no "hair" - no spin or charge to worry about. The simple case.

Whether tidal forces rip the tether apart depends on the size/mass of the hole - around a supermassive black hole, for example, the event horizon is so far from the singularity that there are almost no tidal forces to speak of. Entire planets and stars can pass through the event horizon without getting ripped apart. The smaller the hole, the greater the tidal differences as you approach the horizon.

 

[tomBitonti]

If it has such. In the business, when you're talking to non-specialists and say, "A black hole", we generally assume one that has no "hair" - no spin or charge to worry about. The simple case.

Whether tidal forces rip the tether apart depends on the size/mass of the hole - around a supermassive black hole, for example, the event horizon is so far from the singularity that there are almost no tidal forces to speak of. Entire planets and stars can pass through the event horizon without getting ripped apart. The smaller the hole, the greater the tidal differences as you approach the horizon.

Good catch that (on the size). But, if the upper end was in a stable orbit, and the lower end "close", wouldn't the stresses still become too large to maintain the tether? I also worry about the "no stable orbits" where the escape velocity is > 0.5c.

I understood that charged black holes (very appreciably charged ones, at least), were though to be rare, but there were lots of spinning ones?

Thx!

TomB

 

[Morrus]

Without diving into the actual physics of the thing, I think the biggest obstacle to your idea is that, while a Space Elevator would be going faster at it's top than at it's bottom (Much like a record has to go faster at the outer edge than in the center) the over all gain in speed, while impressive to us mere mortals, is absolute peanuts when compared to the speed of light itself.

Thus, any time difference would be on such a small scale as to make no real difference at all.

As for anchors down black holes... (I'm about to get this possibly very wrong, so forgive me if I do) I think you have to treat the anchor as being part of the system to which it is attached. In other words, you aren't just dropping the anchor, but the anchor, it's chain and the ship to which it is attached as one whole unit. I believe that when the anchor enters the event horizon you have to consider that the whole system has therefore entered the event horizon.

That is my, non-refundable and entirely overvalued, two cents.

GPS satellites in geosynchronous orbit (which is the same thing - the elevator part doesn't matter) have to take the relativistic time differential into account -- and that's just around Earth.

I've no idea how an event horizon interacts with that though. Presumably the tidal forces rip the elevator to shreds, rendering the point moot - but around a large enough black hole you can cross the event horizon and not even notice it.

 

[Fiddleback]

And that's why my two cents are non-refundable.

 

[Umbran]

Good catch that (on the size). But, if the upper end was in a stable orbit, and the lower end "close", wouldn't the stresses still become too large to maintain the tether?

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.

I also worry about the "no stable orbits" where the escape velocity is > 0.5c.

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.

I understood that charged black holes (very appreciably charged ones, at least), were though to be rare, but there were lots of spinning ones?

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.