Mass in asymptotically locally hyperbolic 2+1 gravity is a minimised functional, not a single conserved number, and gluing theorems can construct initial data realising every mass aspect function.
The Constraint Equations
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abstract
We review the properties of the constraint equations, from their geometric origin in hypersurface geometry through to their roles in the Cauchy problem and the Hamiltonian formulation of the Einstein equations. We then review properties of the space of solutions and construction techniques, including the conformal and conformal thin sandwich methods, the thin sandwich method, quasi-spherical and generalized QS methods, gluing techniques and the Corvino-Schoen projection.
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Hyperbolic Mass in 2+1 Dimensions
Mass in asymptotically locally hyperbolic 2+1 gravity is a minimised functional, not a single conserved number, and gluing theorems can construct initial data realising every mass aspect function.