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∗ close to the Planck mass mPl, i.e. m2∗ = O(αm2Pl), we argue that there is electric charge Zc, which, primarily, is due to the formation of a pion condensate (Zc ≅ 0.5α−1e, where α is the fine structure constant and e is the electric charge of the positron). If the charge of the “star” is larger than Zc 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 Zc ≅ α−1e. Astrophysical and cosmological abundances of charged compact boson stars are briefly discussed in terms of dark matter.
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