Have you ever heard of conservation of energy?
Suffice it to say that it is a fundamental principal of reality that you can.
I doubt the GEF's could cut energy emissions down to 0%, however I bet they could last long enough to float to some random star, refuel, then push off again.
I have heard of entropy which says it's a fundamental principal of reality that the very act of conserving energy makes it useless. An imbalance of something is needed to power something with energy. But doing so will move the imbalance towards balance, and once balance is complete, you can't do anything with the energy anymore.
A lake in the mountains can power a wheel placed in the river going downhill to convert gravity into circular movement (and some heat from friction). But if all the water is at the same level, that doesn't work, because you'd need to spend all energy gained by this process into getting the water high enough to fall in the first place.
In other words, if you want to conserve energy 100% in useable forms, you will spend all the energy you have to do so. Nothing left over for luxurious things like being alive.
Life only works on earth because the sun keeps pumping energy into the planet. Remove that outside energy source, and life wouldn't exist because it uses too much energy to support itself.
They might be able to pack enough fuel to go hopping from star to star, yes. But then each time they're at a star, they'd tempt fate again to be found by the shivans. Still, better odds that squatting on a planet.
