Numerical Boson Stars with a Single Killing Vector II: the D=3 Case

TL;DR

This paper numerically constructs 2+1 dimensional boson stars with negative cosmological constant, revealing unique properties such as a finite energy density limit and a smooth horizon, differing from higher-dimensional cases.

Contribution

It extends the analysis of boson stars to three dimensions, showing their distinct features and the transition to extremal BTZ black holes, with implications for holographic duality.

Findings

Existence of a finite central energy density limit.

Scalar field remains smooth inside the horizon.

Monotonic behavior of mass and angular momentum with energy density.

Abstract

We complete the analysis of part I in this series (Ref. \cite{Stotyn:2013yka}) by numerically constructing boson stars in 2+1 dimensional Einstein gravity with negative cosmological constant, minimally coupled to a complex scalar field. These lower dimensional boson stars have strikingly different properties than their higher dimensional counterparts, most noticeably that there exists a finite central energy density, above which an extremal BTZ black hole forms. In this limit, all of the scalar field becomes enclosed by the horizon; it does not contract to a singularity, but rather the origin remains smooth and regular and the solution represents a spinning boson star trapped inside a degenerate horizon. Additionally, whereas in higher dimensions the mass, angular momentum, and angular velocity all display damped harmonic oscillations as functions of the central energy density, in $D=3$ these quantities change monotonically up to the bound on the central energy density. Some implications for the holographic dual of these objects are discussed and it is argued that the boson star and extremal BTZ black hole phases are dual to a spontaneous symmetry breaking at zero temperature but finite energy scale.