Another Mass Gap in the BTZ Geometry?

TL;DR

This paper investigates the existence of rotating hairy black holes and boson stars in 2+1-dimensional spacetimes, finding a mass gap that prevents their formation in certain regimes, especially in the BTZ background.

Contribution

It provides the first perturbative analysis of rotating hairy black holes and boson stars in 2+1 dimensions, revealing non-existence in the perturbative regime and exploring solutions in various backgrounds.

Findings

No hairy black holes in 2+1-dimensions perturbatively.

Boson stars cannot exist in the zero-mass BTZ background.

Constructed boson stars in AdS_3 and conical singularity backgrounds.

Abstract

We attempt the construction of perturbative rotating hairy black holes and boson stars, invariant under a single helical Killing field, in 2+1-dimensions to complete the perturbative analysis in arbitrary odd dimension recently put forth in \cite{Stotyn:2011ns}. Unlike the higher dimensional cases, we find evidence for the non-existence of hairy black holes in 2+1-dimensions in the perturbative regime, which is interpreted as another mass gap, within which the black holes cannot have hair. The boson star solutions face a similar impediment in the background of a conical singularity with a sufficiently high angular deficit, most notably in the zero-mass BTZ background where boson stars cannot exist at all. We construct such boson stars in the AdS_3 background as well as in the background of conical singularities of periodicities \pi,2\pi/3,\pi/2.