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

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

2009-03-12

arxiv.org/abs/0903.2128v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages; uses revtex4; V2: added 1 very important reference; significantly expanded discussion; many small changes in the text

Scientific paper

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.

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