Asymptotic gluing of asymptotically hyperbolic solutions to the Einstein constraint equations

TL;DR

This paper demonstrates a method to connect asymptotically hyperbolic solutions of Einstein's constraint equations with constant mean curvature, enabling the construction of larger solutions from smaller ones by gluing their asymptotic regions.

Contribution

It introduces a novel gluing technique for asymptotically hyperbolic Einstein constraint solutions with constant mean curvature, expanding the toolkit for constructing complex spacetime models.

Findings

Successful gluing of asymptotically hyperbolic solutions demonstrated

Preservation of asymptotic properties after gluing

Potential applications in constructing new solutions to Einstein's equations

Abstract

We show that asymptotically hyperbolic solutions of the Einstein constraint equations with constant mean curvature can be glued in such a way that their asymptotic regions are connected.