On the Global Evolution Problem in 2+1 Gravity
Lars Andersson
Abstract:
We prove global existence in constant mean curvature gauge for the
evolution problem for 2+1 dimensional vacuum Einstein equations,
with data given on a compact orientable surface.
A reduction of the 2+1 vacuum Einstein equations
gives a Hamiltonian system on the cotangent bundle of Teichmuller space
and this plays a central role in the proof.
The 3+1 dimensional Einstein vacuum equations lead, in the presence of a
spatial Killing field, to 2+1 dimensional Einstein equations with matter.
Therefore the 2+1 vacuum case can be viewed as a test case for the 3+1
dimensional, 1 Killing field, evolution problem.