Is there a limit to the energy density of a battery? Better battery technology is very important today: improving the energy stored per volume or mass.  This led me to wonder whether there is a theoretical limit.  (I'm not expecting that we are at all close to it.  Real life just inspired the question.)
One extreme battery would have a reservoir of anti-matter which it could combine with ordinary matter in a controlled fashion.  Could anything beat that for stored energy per mass?
 A: If you put a maximum amount of energy in a volume you get a black hole. Note a black hole can be used as a battery because the energy will be released as hawking radiation which can be used to do work.  The limit to the maximally dense battery then is the Schwarzschild limit $r=2GM/c^2$ and $E=Mc^2 $ so $r=2GE/c^4$.
A: For a battery powered by electrochemistry, there will be a natural limit on its energy density of the following form:
Batteries work by capturing and diverting the electron transfers occurring in chemical reactions that happen in solution (commonly). This means that a chunk of, say, zinc metal in a zinc-copper battery has a certain number of charge units (of electrons) which it releases at a certain voltage. the charge transfer is current and current times voltage is power; divide by the density of zinc and now you have some number which represents the maximum theoretical electrochemical power density of zinc metal on a per-kilogram basis.
To fully exploit that power density requires the invention of a battery consisting almost entirely of replaceable chunks of zinc metal and an electrochemical reaction with no resistive losses- neither of which are possible today.
