Time-dependent solutions of 2+1 gravity

Time-dependent solutions of 2+1 gravity are found for N particles on a sphere with g handles. The theory is reduced to a constrained Hamiltonian system with a finite number of global observables. These include three-vectors that give the spacetime position of each particle, and others that are related to the Teichm\"uller parameters. With these global observables, the dynamical equations (d²{x}ⁱdt²=0) decouple. The cases of the torus and uniformly expanding sphere with N sources are shown to agree with solutions from the metric formulation.