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On Asymptotically Locally Hyperbolic Metrics with Negative Mass
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We construct families of asymptotically locally hyperbolic Riemannian metrics with constant scalar curvature (i.e., time symmetric vacuum general relativistic initial data sets with negative cosmological constant), with prescribed topology of apparent horizons and of the conformal boundary at infinity, and with controlled mass. In particular we obtain new classes of solutions with negative mass.
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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.
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