Charged Boson Stars and Vacuum Instabilities

We consider charged boson stars and study their effect on the structure of the vacuum. For very compact particle like ``stars", with constituent mass $m_{*}$ close to the Planck mass $m_{Pl}$, i.e. $m_{*}^{2} = {\cal O} (\alpha m_{Pl}^{2})$, we argue that there is a limiting total electric charge $Z_c$, which, primarily, is due to the formation of a pion condensate ($Z_{c} \simeq 0.5\alpha^{-1}e$, where $\alpha$ is the fine structure constant and $e$ is the electric charge of the positron). If the charge of the ``star" is larger than $Z_c$ we find numerical evidence for a complete screening indicating a limiting charge for a very compact object. There is also a less efficient competing charge screening mechanism due to spontaneous electron-positron pair creation in which case $Z_{c} \simeq \alpha^{-1}e$. Astrophysical and cosmological abundances of charged compact boson stars are briefly discussed in terms of dark matter.