  Consider a rotating and possibly pulsating "star" in (2+1) dimensions. If the
star is axially symmetric, then in the vacuum region surrounding the star, (a
region that we assume at most contains a cosmological constant), the Einstein
equations imply that under physically plausible conditions the geometry is in
fact stationary. Furthermore, the geometry external to the star is then
uniquely guaranteed to be the (2+1) dimensional analogue of the Kerr-de Sitter
spacetime, the BTZ geometry. This Birkhoff-like theorem is very special to
(2+1) dimensions, and fails in (3+1) dimensions. Effectively, this is a "no
hair" theorem for (2+1) dimensional axially symmetric stars: the exterior
geometry is completely specified by the mass, angular momentum, and
cosmological constant.
