Born-Infeld boson stars

We study the Einstein-Klein-Gordon system coupled to the Born-Infeld electrodynamics. We explore the solution space of a static spherically symmetric, complex scalar field minimally coupled to both gravitational and electromagnetic fields. The resulting asymptotically flat solutions resemble the known charged boson stars in Maxwell electrodynamics. The behaviour of such configurations as a function of the Born-Infeld parameter $b$ and the scalar field charge parameter $q$ has been analyzed. Given $b$, a critical value for $q$ exists beyond which no static solutions exist, we find that the value of this critical charge increases with respect to the Maxwell case ($b\to\infty$) as $b$ decreases. We also found that Born-Infeld boson stars have lower mass for any finite value of the Born-Infeld parameter and that their compactness is lower than Maxwell's counterparts.