Potential energy conservation in traversable wormholes Let's say I have a tube, of large radius (about 5 - 7 meters in diameter), with traversable wormholes at the ends. The wormholes are arranged as such that if something falls inside one hole from inside of the tube, it will come out at the other end still inside the tube. Now, let's say I empty all air from the tube (to make a "vacuum tube," if you will), set it upright and somehow manage to get a rock (or whatever other object) in there. My question now is, does the situation described above rule out the existence of traversable wormholes?
Or, if not, since the rock is falling through the wormhole over and over again, will it always be accelerating at the same rate? Or will its velocity only always be approaching light speed? In either case, would the rock's mass increase to the point that it overpowers Earth's gravity, or even collapses into a singularity? Or is there something that would prevent that from happening?
 A: I found an entry in a Wormhole FAQ that seems to address your thought experiment:
"Is a wormhole whose mouths are arranged vertically in a gravitational field a source of unlimited energy?
No.  The argument in favor of such a wormhole being an energy source is this:  An object falls from the upper mouth, gains kinetic energy as it falls, enters the lower mouth, reemerges from the upper mouth with this newly acquired kinetic energy, and repeats the cycle to gain even more kinetic energy ad infinitum. The problem with this is that general relativity does not permit discontinuities in the metric – the descriptor of the geometry of spacetime.  This means that the gravitational potential of an object at the lower mouth must continuously rise within the wormhole to match the potential it had at the upper mouth.  In other words, this traversal of the wormhole is “uphill” and therefore requires work.  This work precisely cancels the gain in kinetic energy."  
A: I'm no GR whiz, so this answer may be wrong. Comments appreciated.
There are three things I see here. The first issue is that wormholes do not (may not) accelerate particles. Yes, while falling in a particle will accelerate; but while popping out, the reverse will happen, giving rise to a zero average acceleration. The exit of a wormhole is just like the entrance; so it will gravitationally attract you inwards.
The second issue is that if the rock does manage to accelerate, it will obtain the energy from the gravitational field. In other words, it's own gravitational effects will counter the wormhole, reducing the 'energy' of the wormhole's field (GR gravitational PE is not well defined, though). What may happen is this:(speculation) A wormhole's throat has a negative energy density. If the energy density becomes positive, the wormhole necks off like a piece of taffy, giving rise to two black holes or just expanding outwards (can't remember which). Popping a rock inside increases the energy density. If the rock keeps accelerating, it will get enough energy at some point or the other to destroy the wormhole.
The third issue is trivial to the paradox but worth mentioning. In relativity, we cannot have a 'constant acceleration' if acceleration is $\frac{d\vec{v}}{dt}$. Since force is $\frac{d\gamma m_0\vec{v}}{dt}$, even with a proportional-to-mass force (like gravity), the acceleration will not be constant and will slow nearly to a standstill as the velocity approaches lightspeed. $\gamma v$ will increase at a constant rate, ($\gamma=\frac{1}{\sqrt{1-v^2/c^2}}$ becomes very large, near lightspeed)
