A Gedanken about Artificial Gravity

[RVM45]

Does the mathematics exist to describe what would happen IF it were possible to perform the folowing experiments?

Assume that you have artificial gravity--the ability to warp space-time AS IF a large mass existed at point X. Let us further suppose that our machine is arbitrarily powerful--as powerful as we decide to turn the "Power Button" to. Let us further suppose that we can project X--The center of gravity for the pseudo-mass we are simulating--to a point at a very large distance from ourselves.

Set X far out in intergalactic space, far away from any measureable quantity of real mass. Set the power level to one galactic mass. Turn the machine on.

Viola', you now have a very massive black hole--once in there is NO out. This is no problem for you; because you've thoughtfully located yourself well outside the swartxchild radius. After a moment, you tire of the experiment and turn the artificial gravity off.

What happens? Can mass now merrily pass through a volume of space that moments before was inside the event horizon? Why? Or why not?

Some folks believe that a black hole warps the space so totally that it breaks loose from the universal space-time and becomes a much smaller "Bubble Universe".

So did we just permanently pinch a big piece of nothing off(or empty space--which may or may not be the same thing)? How bizzarre!

Second experiment: Maintaining the same location and the same X; Hook the gravity switch to some sort of pulse generators that cause it to turn itself on and off at regular intervals--like 60 times a secomd.

What happens now?

Now, completely bored, we hook the gravity machine to a beat box; and have a random number generator to select the beat.

What effect would a galactic mass oscillating in and out of existense to a Tango beat have on the surrounding space time?

While artificial gravity probably isn't possible--I'd still think a good mathematician could work out some of the hypothetical strains and stresses that would result in the surrounding space-time_IF IT WERE.

I would think that any number of interesting/paradoxal situations might be engendered.

....RVM45

 

[GoodGuysEatPie]

Step 1:


If Step 1 is too tedious (like it mostly is for me), try the less tedious, but also fulfilling step by some of the same authors of Step 1:
Exploring Black Holes.

Once those steps are complete, it is possible to move beyond a pop-science approach to GR and black holes.

To speculate on one of your questions: what would happen to space after you remove a black hole suddenly? I think you would still be able to move through that space, no problem. Such a scenario would probably create gravitational waves, but I don't think there would be any irreversible effects.

Now: HOW do you propose creating your artificial space-warper? I realize you were presenting a hypothetical scenario, I just don't see how it could be done without using actual mass. Mass tells space how to bend. Space tells mass how to move. Not sure how to circumvent those rules.

~ggep~

 

[sol invictus]

Does the mathematics exist to describe what would happen IF it were possible to perform the folowing experiments?

The mathematics exists, but what it tells you is that your experiment is impossible. In other words the situation you describe is inconsistent with the equations for gravity.

The reason is that conservation of energy is built in to the equations from the start. You cannot violate it in any solution to those equations. One way to measure the total energy in a region is to look at the gravitational field on a sphere surrounding that region. If the field is non-zero the energy will be non-zero, and so long as no energy passes in or out of that sphere, the energy inside cannot change (that's conservation of energy). Therefore if the machine was off, so that there was no field around it, there is no way you can just flip a switch and turn on the field - that would violate conservation of energy. Put another way, if the machine was capable of producing a field as strong as that of a mass M, then it already had energy M, and therefore already had a field around it.

But if you just want to ask what happens when a black hole disappears, there's a way to ask that which is consistent with gravity. BHs slowly evaporate due to Hawking radiation (their energy passes out through our sphere in the form of radiation). In the end nothing is left of them - just ordinary, flat space plus some very dilute radiation far away.

 

[Ziggurat]

This might get at the poster's question a bit without requiring anything unphysical. If you consider the sun, for example, it's got a gravitational well due to its mass. Is it possible for such a well to exist without that mass being there? Well, in principle, I think so: focus a bunch of gravity waves just so, and for an instant, you could recreate that gravitational well without the mass being there. What happens after that? Well, the gravity waves keep going, the well disappears, and you have an outgoing ripple of spatial distortion.

 

[sol invictus]

This might get at the poster's question a bit without requiring anything unphysical. If you consider the sun, for example, it's got a gravitational well due to its mass. Is it possible for such a well to exist without that mass being there? Well, in principle, I think so: focus a bunch of gravity waves just so, and for an instant, you could recreate that gravitational well without the mass being there. What happens after that? Well, the gravity waves keep going, the well disappears, and you have an outgoing ripple of spatial distortion.

That depends on how well you focus them. Focus them into a small enough radius and you'll make a black hole, in which case they'll get stuck inside.

 

[RecoveringYuppy]

Wouldn't well focused gravity waves give you a localized tidal force and not a gravity well?

 

[RVM45]

I suppose I think too much--but I had read where some physicist believe that anti-gravity machines may be possible--though no one knows how.

Presumably, if you could create anti-gravity you could create artificial gravity.

What I was going on was those rubber sheet diagrams with a cannonball warping the 2-D "Space-Time" of the sheet.

Some folks say that a good way to concieve of a black hole is that the cannon ball drew the sheet down so far that it closed in on itself.

So if you could get a piece of Space-Time completely turned in on itself--while it was empty--then what would you have?

I mean if you have a really big soap film; and someone blows on a small area enough to get it to close in on itself; it forms a soap buble and fies away...

Doubtless my Model is defective somehow...

.....RVM45

 

[sol invictus]

Wouldn't well focused gravity waves give you a localized tidal force and not a gravity well?

Gravity waves carry energy and momentum. A sufficient quantity of any kind of energy in a small enough region will always form a black hole. Gravity couples to itself as well as to matter and radiation.

I mean if you have a really big soap film; and someone blows on a small area enough to get it to close in on itself; it forms a soap buble and fies away...

Doubtless my Model is defective somehow...

Such a thing is not impossible. The problem, however, is that it is unlikely anyone will ever know. The only way to find out is to jump into a black hole, and once you're inside you cannot get out again.

 

[MattusMaximus]

I suppose I think too much--but I had read where some physicist believe that anti-gravity machines may be possible--though no one knows how.

Do you have a link or reference on this? It would certainly help move the conversation along.

 

[DrBaltar]

I think you'd get a lot of angry extraterrestrials telling you to cut that ◊◊◊◊ out.

 

[Roboramma]

I'm a little unclear here, but doesn't a black hole move through space-time?
So the space-time around a black hole would be like a wave moving over water, and the place where it was before "smooths out".

I mean, a black hole isn't always in the same region of space-time, right?

 

[Complexity]

I'm a little unclear here, but doesn't a black hole move through space-time?
So the space-time around a black hole would be like a wave moving over water, and the place where it was before "smooths out".

I mean, a black hole isn't always in the same region of space-time, right?

Things don't move within space-time - they are within space-time.

Don't forget that time is one of the dimensions of space-time.

Space-time is a fixed, unchanging thing.

 

[sol invictus]

I'm a little unclear here, but doesn't a black hole move through space-time?
So the space-time around a black hole would be like a wave moving over water, and the place where it was before "smooths out".

I mean, a black hole isn't always in the same region of space-time, right?

As complexity says it doesn't make a lot of sense to think about motion in spacetime. A particle, as it moves through time (and possibly space), sweeps out a line in spacetime - that's called the worldline of the particle. A black hole sweeps out a worldvolume.

But to answer what I think was your question, yes, BHs can move through space. It's true that, as viewed by a stationary observer, a BH leaves a kind of gravitational wake behind it. If the hole is moving very fast the wake becomes a shockwave, not unlike a sonic boom. Still, if you passed through the shock into the space behind the hole, you wouldn't find anything particularly strange there.

BHs are a lot less weird than most people seem to think. One thing to bear in mind is that the gravitational field around a BH is absolutely identical to the field outside a star (or any other symmetric mass distribution) of the same total mass and angular momentum.

 

[Roboramma]

Things don't move within space-time - they are within space-time.

Don't forget that time is one of the dimensions of space-time.

Space-time is a fixed, unchanging thing.

Because motion requires a change in time! I feel dumb.

 

[Roboramma]

As complexity says it doesn't make a lot of sense to think about motion in spacetime. A particle, as it moves through time (and possibly space), sweeps out a line in spacetime - that's called the worldline of the particle. A black hole sweeps out a worldvolume.

That makes sense, but, now I'm finding this weird. If the black hole (or whatever object, we could be talking about a planet or star for the purposes of what I'm going to say, wasn't there before, clearly the curvature was different in the past, right?
I mean, if gravity is basically the curvature of space-time, then the curvature has to be changeable?
And if it changes as things form, doesn't it change as they move?

I've never really been able to fully get my head around spacetime. On the one hand, motion is time dependant, so how can something move through spacetime? On the other, it seems that if things aren't moveing through spacetime, they can't really follow lines through spacetime, and I thought the whole point of general relativity was that things follow the shortest line through spacetime (maybe that's an oversimplification).

Anyway, I don't pretend to have much of a grasp of this, but your posts are helping.

But to answer what I think was your question, yes, BHs can move through space. It's true that, as viewed by a stationary observer, a BH leaves a kind of gravitational wake behind it. If the hole is moving very fast the wake becomes a shockwave, not unlike a sonic boom. Still, if you passed through the shock into the space behind the hole, you wouldn't find anything particularly strange there.

BHs are a lot less weird than most people seem to think. One thing to bear in mind is that the gravitational field around a BH is absolutely identical to the field outside a star (or any other symmetric mass distribution) of the same total mass and angular momentum.

That all makes sense. The shockwave thing is cool, though - would a star moving fast enough also leave a shockwave?