On Asymptotically Locally Hyperbolic Metrics with Negative Mass

TL;DR

This paper constructs new families of asymptotically locally hyperbolic metrics with constant scalar curvature, allowing for prescribed topology and negative mass, contributing to the understanding of geometric structures in general relativity.

Contribution

It introduces novel constructions of asymptotically locally hyperbolic metrics with negative mass and specified topological features, expanding the known solution space.

Findings

Existence of new metrics with negative mass

Control over topology of horizons and boundary

Metrics with prescribed conformal boundary

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.