A density theorem for asymptotically hyperbolic initial data satisfying the dominant energy condition

Abstract

When working with asymptotically hyperbolic initial data sets for general relativity it is convenient to assume certain simplifying properties. We prove that the subset of initial data with such properties is dense in the set of physically reasonable asymptotically hyperbolic initial data sets. More specifically, we show that an asymptotically hyperbolic initial data set with non-negative local energy density can be approximated by an initial data set with strictly positive local energy density and a simple structure at infinity, while changing the mass arbitrarily little. The argument follows an argument used by Eichmair, Huang, Lee, and Schoen in the asymptotically Euclidean case