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.
Exotic hyperbolic gluings
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We carry out "exotic gluings" a la Carlotto-Schoen for asymptotically hyperbolic general relativistic initial data sets. In particular we obtain a direct construction of non-trivial initial data sets which are exactly hyperbolic in large regions extending to conformal infinity.
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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.