On Asymptotically Locally Hyperbolic Metrics with Negative Mass

Abstract

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.