Computer Science
Scientific paper
Jan 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phdt........23w&link_type=abstract
Ph.D. Thesis Texas Univ., Austin.
Computer Science
Boundary Value Problems, Gravitation, Minkowski Space, Space-Time Functions, Time Dependence, Center Of Mass, Hamiltonian Functions, Polygons, Quantum Theory, Spheres
Scientific paper
A new formulation is proposed of 2+1 gravity with a finite number of variables which described directly the observable properties of space-time. A surface is described as a nonplanar polygon embedded in Minkowski space, with an even number of edges that are identified two by two. As this polygon evolves in time, it carves a tube out of Minkowski space, with pairs of walls that are to be glued together. The theory is presented in the constrained Hamiltonian formulation. The initial value problem and the dynamical equations are solved for a sphere with g handles and N point particles, and for a plane with g wormholes and N particles. The total mass, which in the static case is just 2 pi times the Euler number, is computed for various time dependent solutions. A sphere with N moving particles has a total mass less than 4 pi; conversely for particles on a plane the total mass increases with velocity. A sphere with one or more handles can accommodate a particle with a deficit angle up to 2 pi, not included. Properties are discussed of the center of mass motion and relative motion.
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