Birkhoff-like theorem for rotating stars in (2+1) dimensions

Understand

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.