Gauss-Bonnet boson stars with a single Killing vector

Abstract

We construct asymptotically anti--de Sitter boson stars in Einstein-Gauss-Bonnet gravity coupled to a $\frac{D\ensuremath{-}1}{2}$-tuplet of complex massless scalar fields both perturbatively and numerically in $D=5,7,9,11$ dimensions. These solutions possess just a single helical Killing symmetry due to the choice of scalar fields. The energy density at the center of the star characterizes the solutions, and for each choice of the Gauss-Bonnet coupling $\ensuremath{\alpha}$ we obtain a one parameter family of solutions. All solutions respect the first law of thermodynamics, in the numerical case to within 1 part in $1{0}^{6}$. We describe the dependence of the angular velocity, mass, and angular momentum of the boson stars on $\ensuremath{\alpha}$ and on the dimensionality. For $D\ensuremath{\ge}7$ these quantities reach maximum values and then decrease to eventually approach finite values as the central energy density tends to infinity. In the limit of diverging central energy density, the Kretschmann invariant at the center of the boson star also diverges. This is in contrast to the $D=5$ case, where the Kretschmann invariant diverges at a finite value of the central energy density.