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For a compact connected orientable n-manifold M, n≥3, we study the structure of classical superspace S≡M/D, quantum superspace S0≡M/D0, classical conformal superspace C≡M/P/D, and quantum conformal superspace C0≡M/P/D0. The study of the structure of these spaces is motivated by questions involving reduction of the canonical Hamiltonian formulation of general relativity to a non-degenerate...
For the problem of the Hamiltonian reduction of Einstein’s equations on a 3+1 vacuum spacetime that admits a foliation by constant mean curvature (CMC) compact spacelike hypersurfaces M that satisfy certain topological restrictions, we introduce a dimensionless non-local time-dependent reduced Hamiltonian system $$ H_{reduced} :R^ - \times P_{reduced} \to R $$ where the reduced Hamiltonian is given...
We consider the problem of the Hamiltonian reduction of Einstein's equations on a (3 + 1)-vacuum spacetime that admits a foliation by constant mean curvature (CMC) compact spacelike hypersurfaces M that satisfy certain topological restrictions. After a conformal reduction process, we find that the Einstein flow is described by a dimensionless non-local time-dependent Hamiltonian system where R ...
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