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On the global evolution problem in 2+1 gravity

Lars Andersson·Vincent Moncrief·Anthony J. Tromba
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Abstract

Existence of global CMC foliations of constant curvature 3-dimensional maximal globally hyperbolic Lorentzian manifolds, containing a constant mean curvature hypersurface with $\genus(Σ) > 1$ is proved. Constant curvature 3-dimensional Lorentzian manifolds can be viewed as solutions to the 2+1 vacuum Einstein equations with a cosmological constant. The proof is based on the reduction of the corresponding Hamiltonian system in constant mean curvature gauge to a time dependent Hamiltonian system on the cotangent bundle of Teichmüller space. Estimates of the Dirichlet energy of the induced metric play an essential role in the proof.

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Lars Andersson, Vincent Moncrief, Anthony J. Tromba. 1996-10-10. On the global evolution problem in 2+1 gravity. https://doi.org/10.1016/s0393-0440(97)87804-7

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