More on massive 3D gravity

Abstract

We explore the space of static solutions of the recently discovered three-dimensional ``new massive gravity'' (NMG), allowing for either sign of the Einstein-Hilbert term and a cosmological term parametrized by a dimensionless constant $\ensuremath{\lambda}$. For $\ensuremath{\lambda}=\ensuremath{-}1$ we find black hole solutions asymptotic (but not isometric) to the unique (anti) de Sitter [(A)dS] vacuum, including extremal black holes that interpolate between this vacuum and $(\mathrm{A}){\mathrm{dS}}_{2}\ifmmode\times\else\texttimes\fi{}{S}^{1}$. We also investigate unitarity of linearized NMG in (A)dS vacua. We find unitary theories for some dS vacua, but (bulk) unitarity in AdS implies negative central charge of the dual conformal field theories (CFT), except for $\ensuremath{\lambda}=3$ where the central charge vanishes and the bulk gravitons are replaced by ``massive photons.'' A similar phenomenon is found in the massless limit of NMG, for which the linearized equations become equivalent to Maxwell's equations.