Would wormholes transmit gravity, if so how?

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Would wormholes transmit gravity, if so how? Seeing as wormholes transmitting gravity would prevent them from being used as a perpetual motion device, generating increasingly more kinetic energy, the way they are in the video game "Portal", and since they would transmit matter, it would stand to reason that wormholes do transmit gravity, meaning that you could feel the strength of the gravitational field at mouth A when you're in the vicinity of mouth B.

But how would this work exactly? Would the field fall off according to the interior length of the wormhole (a useful wormhole has an interior length that's less than the distance between A and B in normal space)?

If so, what would happen if I did the following:

1) Open a wormhole with mouth A near a massive star's surface and mouth B at a distance from the star that's so far away that in normal space only 0.01% of the star's surface gravity remains.

2) I made the wormhole such that it's interior length is large enough that I do not travel backwards in time (to avoid opening that can of worms), but still shorter than the normal space distance between A and B, say half the length).

3) I then catapult a mass into the mouth at A with a speed that's just enough to overcome the gravitational field inside the wormhole (it falls from 100% at A to roughly 25% at B), so the mass stands still for a split second after it exits mouth B.

4) I then collapse the wormhole and leave the mass to fall back unto the star's surface.

Naively I would expect the mass to gather more kinetic energy (because it falls from 0% field strength at B to 100% field strength at A while it only overcame 75% of the field strength to get from A to B). Repeating the whole process would then heat the star with no effort, free energy. What am I missing here (does a wormhole "suck in" extra gravitons so the gravitational gradient inside the wormhole is ultimately equal to the one outside, the same as what happens when you make a shortcut in fluid dynamics?) or does this prove traversable wormholes don't exist?

P.S. alternatively, in step 4) I could collapse the wormhole, start an engine that's attached to the mass for a brief moment to overcome the last 0.01% of the gravitational field and fly away from the star, reaching the next star with less total energy consumption than it would have taken without using a wormhole. I could even construct gravity cannons using this method, hurling masses between two planets, collecting the energy of the surface impacts and use part of that energy to hurl new masses, generating net power in the process.
 
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pervect
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If you consider geometries that are static so that potential functions exist at all, I'd expect wormholes to have multi-valued potential functions.

So the good news is you can express the acceleration of gravity (relative to the static geometry) as the gradient of some potential function, the bad news is that if your path traverses the wormhole, the value of this function (energy) won't return to it's initial value but will depend on the winding number of how often the path goes through the wormhole.

It's hard to find a detailed reference on this, though.

Some of the ideas that lead to this conclusion are discussed in Cramer's Alternate View columns on wormholes, such as http://www.npl.washington.edu/av/altvw69.html

Basically, if an electromagnetic charge passes through a wormhole, Cramer's arguments shows that you expect it to drag electromagnetic field lines through it.

Similar arguments suggest that a mass dragged through a wormhole will behave similarly

Cramer said:
If a positive electric charge Q passes through a wormhole mouth, the electric lines of force radiating away from the charge must thread through the aperture of the wormhole. The net result is that the entrance wormhole mouth has lines of force radiating away from it, and the exit wormhole mouth has lines of force radiating toward it. In effect, the entrance mouth has now been given a positive electric charge Q, and the exit mouth acquires a corresponding negative charge -Q. Similarly, if a mass M passes through a wormhole mouth, the entrance mouth has its mass increased by M, and the exit mouth has its mass reduced by an amount -M.
If the path through the external space-time has a fixed gravitational potential difference, and the path through the wormhole itself has a potential difference that starts at zero (assuming that you start with a symmetrical wormhole - but ultimately depends on the history of what objects have passed through it and in which direction), it becomes pretty clear that integrating around a loop that passes through the wormhole isn't guaranteed to give a globally vanishing potential function / energy.

At least one semi-popular book claims otherwise, but I find the arguments raised by Cramer et al convincing.

Note that there is an applicable notion of energy to this particular circumstance though (due to the assumption that the space-time is static) and that giving some external object energy will cause the wormhole mouths to loose mass resulting in the applicable notion of total energy being conserved.
 
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Roger Penrose believes that gravitational signatures can even transit the big bang; that is, some gravitational characteristics from before the big bang can be found within CMBR....
 
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If the path through the external space-time has a fixed gravitational potential difference, and the path through the wormhole itself has a potential difference that starts at zero (assuming that you start with a symmetrical wormhole - but ultimately depends on the history of what objects have passed through it and in which direction), it becomes pretty clear that integrating around a loop that passes through the wormhole isn't guaranteed to give a globally vanishing potential function / energy.

At least one semi-popular book claims otherwise, but I find the arguments raised by Cramer et al convincing.

Note that there is an applicable notion of energy to this particular circumstance though (due to the assumption that the space-time is static) and that giving some external object energy will cause the wormhole mouths to loose mass resulting in the applicable notion of total energy being conserved.
So it would appear as generating free energy but it would really be tapping into the energy of the wormhole? Does this energy come from the device that is keeping the wormhole open (meaning it would take more energy to keep a wormhole open if heavy objects pass through it even though the radius of the wormhole does not change)? Does that imply that naturally occuring wormholes would collapse after a certain amount of mass has traveled through it? It does sound like a very elegant solution.
 

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