Rotating Boson Stars in 2+1 Dimensions

TL;DR

This work analyzes rotating boson stars in (2+1)-dimensional anti-de Sitter space with negative cosmological constant, formulating a rotating ansatz for the metric and a harmonic time- and azimuth-dependent complex scalar field. The coupled Einstein-scalar system is solved numerically, and masses and angular momenta are computed through holographic counterterms, yielding $\bar M=\frac{2M-1}{8G}$ and $\bar J=\frac{J}{4G}$, with no regular flat-space limit $\Lambda \to 0$. The solutions form a continuous family labeled by the vorticity $k$, node number $n$, and central amplitude, featuring differential rotation and ring-like energy densities for $|k|>1$, and their properties are discussed in the AdS/CFT context via boundary stress-tensor data. The paper also comments on charged extensions and outlines how these configurations fit into broader holographic and gravitational frameworks.

Abstract

We consider rotating boson star solutions in a three-dimensional anti-de Sitter spacetime and investigate the influence of the rotation on their properties. The mass and angular momentum of these configurations are computed by using the counterterm method. No regular solution is found in the limit of vanishing cosmological constant.