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- W14389729 abstract "When the vacuum Einstein equations are cast in the form of hamiltonian evolution equations, the initial data lie in the cotangent bundle of the manifold MSigma of riemannian metrics on a Cauchy hypersurface Sigma. As in every lagrangian field theory with symmetries, the initial data must satisfy constraints. But, unlike those of gauge theories, the constraints of general relativity do not arise as momenta of any hamiltonian group action. In this paper, we show that the bracket relations among the constraints of general relativity are identical to the bracket relations in the Lie algebroid of a groupoid consisting of diffeomorphisms between space-like hypersurfaces in spacetimes. A direct connection is still missing between the constraints themselves, whose definition is closely related to the Einstein equations, and our groupoid, in which the Einstein equations play no role at all. We discuss some of the difficulties involved in making such a connection." @default.
- W14389729 created "2016-06-24" @default.
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- W14389729 date "2010-03-15" @default.
- W14389729 modified "2023-09-27" @default.
- W14389729 title "Groupoid symmetry and constraints in general relativity. 1: kinematics" @default.
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