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On the global evolution problem in 2 + 1 gravity

✍ Scribed by Lars Anderson; Vincent Moncrief; Anthony J. Tromba

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
823 KB
Volume
23
Category
Article
ISSN
0393-0440

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✦ Synopsis

Existence of global constant mean curvature (CMC) foliations of constant curvature 3dimensional maximal globally hyperbolic Lorentzian manifolds, containing a constant mean cur- vature hypersurface with genus(C) > I, 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 CMC gauge to a time-dependent Hamiltonian system on the cotangent bundle of Teichmiiller space. Estimates of the Dirichlet energy of the induced metric play an essential role in the proof.

πŸ“œ SIMILAR VOLUMES

The radial gauge in 2 + 1 dimensional gr
The radial gauge in 2 + 1 dimensional gravity
✍ P Menotti; D Seminara πŸ“‚ Article πŸ“… 1991 πŸ› Elsevier Science 🌐 English βš– 921 KB

Some features of the radial gauge which are special of 2 + 1 dimensions are used to calculate classical solutions of Einstein's equations in 2 + 1 dimensions. In addition to already known solutions we find new time independent and time dependent solutions both of point-like and extended nature.