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 ∗ close to the Planck mass m Pl , i.e. m 2 ∗ = O(αm 2 Pl) , we argue that there is electric charge Z c , which, primarily, is due to the formation of a pion condensate ( Z c ≅ 0.5 α −1 e, 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 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 ≅ α −1 e. Astrophysical and cosmological abundances of charged compact boson stars are briefly discussed in terms of dark matter.