Another Mass Gap in the BTZ Geometry?

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 π,2π/3,π/2.

13 pages, 2 appendices, Invited Contribution to an IOP special volume of Journal of Physics A in honor of Stuart Dowker's 75th birthday, v2: discussion in section 4 expanded

References in corpus (4)

• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Symmetries of Higher Dimensional Black Holes
• Hairy black holes and solitons in global AdS 5
• Closed String Tachyons on AdS Orbifolds and Dual Yang-Mills Instantons

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• A rotating hairy AdS3 black hole with the metric having only one Killing vector field
• Gauss-Bonnet Boson Stars with a Single Killing Vector
• Reentrant phase transitions in Einstein-Maxwell-scalar black holes
• Numerical Boson Stars with a Single Killing Vector II: the D=3 Case
• Exact Solutions and Black Hole Stability in Higher Dimensional Supergravity Theories