It could be easier to enclose your charging station in a different gravitation field. Let time dilation work to your advantage. Instead of infinite current, you need merely an anti-gravity device. Unlike infinite speed which relativity say you cannot have, at least no one yet come up with why anti-gravity cannot exist.
Sooooo... you're saying there's a chance?
Well... my statement was "at least no one
yet come up with why anti-gravity cannot exist." Key word there being
yet.
So, to answer that, we will first have to invent anti-gravity - to see if there is any physical laws preventing that from happening.
There is always a chance. I just wont bet on it happening.
Quantum mechanics say you can find the electron tunneling elsewhere by itself - that is, finding an electron moved somewhere (with higher energy potential) all by itself. So, there is a chance that all a sudden, an ungodly amount of electron tunneled into your battery by itself.
Now, by the same reasoning, there is a chance that you would suddenly suffocate in your house. Air molecules moves randomly. There is a chance that all the molecules moving randomly but randomly away from where you are. So poof, no more you. There is a chance...
Chance doesn't mean squat. There is even a chance another big bang occurring near us before you read this reply - no more you, no more me, no more eevblog...
I'm not giving up hoping, there is always a chance...