Charged Boson Stars and Vacuum Instabilities

Abstract

We consider charged boson stars and study their effect on the structure of the vacuum. For very compact particle like ``stars", with constituent mass $m_{\ast }$ close to the Planck mass $m_{Pl}$, i.e. $m_{\ast }^2=\mathcal{O}(\hat{I}\pm m_{Pl}^2)$, we argue that there is a limiting total electric charge $Z_c$, which, primarily, is due to the formation of a pion condensate ($Z_c\simeq 0.5\hat{I}{\pm }^{-1}e$, where $\hat{I}\pm$ 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 $Z_c\simeq \hat{I}{\pm }^{-1}e$. Astrophysical and cosmological abundances of charged compact boson stars are briefly discussed in terms of dark matter.

latex,29p,9 figs not included can be sent by fax on request,ITP 92-24,ZU-TH-38/92