Seminarium Teorii Względności i Grawitacji

In arXiv:0910.187, Isenberg, Lee, and Stavrov Allen presented a gluing construction of asymptotically hyperbolic general relativistic initial data sets which can be used to change the topology of the conformal boundary at infinity. The construction was inspired by a similar construction of Maskit in the context of complex geometry. In this work we present two applications of the method: 1) the first proof of positivity of total hyperbolic mass when the conformal boundary has spherical topology without restrictions on the dimension and the interior topology, and 2) a construction of initial data sets with negative total mass for higher genus boundary manifolds. The talk is based on joint work with Erwann Delay.