Numerical Boson Stars with a Single Killing Vector I: the $D\ge5$ Case

TL;DR

This paper numerically constructs higher-dimensional anti-de Sitter boson star solutions with a single helical symmetry, revealing their properties and the transition to black hole formation at high central energy densities.

Contribution

It introduces a new class of boson star solutions in odd dimensions with a single Killing vector, expanding understanding of gravitational solitons in higher dimensions.

Findings

Boson stars form a one-parameter family characterized by central energy density.

As energy density increases, solutions exhibit damped oscillations in physical quantities.

Divergence of the Kretschmann invariant indicates black hole formation at high densities.

Abstract

We numerically construct asymptotically anti-de Sitter boson star solutions using a minimally coupled $\frac{D-1}{2}$-tuplet complex scalar field in $D=5,7,9,11$ dimensions. The metric admits multiple Killing vector fields in general, however the scalar fields are only invariant under a particular combination, leading to such boson star solutions possessing just a single helical Killing symmetry. These boson stars form a one parameter family of solutions, which can be parametrized by the energy density at their center. As the central energy density tends to infinity, the angular velocity, mass, and angular momentum of the boson star exhibit damped harmonic oscillations about finite central values, while the Kretschmann invariant diverges, signaling the formation of a black hole in this limit.